Perimeter of a Parallelogram: Using variables

Question 1

The parallelogram ABCD has a perimeter equal to 80 cm.

Calculate X.

Question 2

A parallelogram has one side that is 2 times longer than the other. The length of the smaller side is X.

Express the circumference of the parallelogram in terms of X.

Question 3

Look at the parallelogram shown below.

AB = 6

AC = X

The perimeter of the parallelogram is 20.

Find X.

Question 4

The longest sides of a parallelogram are X cm long and are four times longer than the shorter sides.

Express the perimeter of the parallelogram in terms of X.

Question 5

ABCD is a parallelogram whose perimeter is equal to 24 cm.

The side of the parallelogram is two times greater than the adjacent side (AB>AD).

CE is the height of the side AB

The area of the parallelogram is 24 cm².

Find the height of CE

Examples with solutions for Perimeter of a Parallelogram: Using variables

Exercise #1

The parallelogram ABCD has a perimeter equal to 80 cm.

Calculate X.

Video Solution

Step-by-Step Solution

Since in a parallelogram each pair of opposite sides are equal and parallel:

$BC=AD=2x$

$AB=CD=x$

Now let's substitute the known data into the formula for calculating the perimeter:

$80=2x\times2+2\times x$

$80=4x+2x$

$80=6x$

Let's divide both terms by 6:

$\frac{80}{6}=\frac{6x}{6}$

$\frac{80}{6}=x$

Let's simplify the fraction by 2

$\frac{40}{3}=x$

Answer

$x=\frac{40}{3}$

Exercise #2

A parallelogram has one side that is 2 times longer than the other. The length of the smaller side is X.

Express the circumference of the parallelogram in terms of X.

Video Solution

Step-by-Step Solution

As is true of a parallelogram each pair of opposite sides are equal to one another

$AB=CD,AC=BD$

Given that $AB > AC$

Let's call AC by the name X and therefore:

$AB=2AC=2\times x=2x$

Now we know that:

$AB=CD=2x,AC=BD=x$

The perimeter is equal to the sum of all the sides together:

$2x+x+2x+x=6x$

Answer

4X+4

Exercise #3

Look at the parallelogram shown below.

AB = 6

AC = X

The perimeter of the parallelogram is 20.

Find X.

Video Solution

Step-by-Step Solution

As is true for a parallelogram each pair of opposite sides are equal:

$AB=CD=6,AC=BD=x$

Calculate X according to the given perimeter:

$20=6+6+x+x$

$20=12+2x$

$20-12=2x$

$8=2x$

$x=4$

Answer

Exercise #4

The longest sides of a parallelogram are X cm long and are four times longer than the shorter sides.

Express the perimeter of the parallelogram in terms of X.

Video Solution

Step-by-Step Solution

In a parallelogram, each pair of opposite sides are equal and parallel: AB = CD and AC = BD.

Given that the length of one side is 4 times greater than the other side equal to X, we know that:

$AB=CD=4AC=4BD$

Now we replace the data in this equation with out own (assuming that AB = CD = X):

$x=x=4AC=4BD$

We divide by 4:

$\frac{x}{4}=\frac{x}{4}=AC=BD$

Now we calculate the perimeter of the parallelogram and express both AC and BD using X:

$P=x+\frac{x}{4}+x+\frac{x}{4}$

$P=2x+\frac{x}{4}+\frac{x}{4}=2\frac{1}{2}x$

Answer

2.5X cm

Exercise #5

ABCD is a parallelogram whose perimeter is equal to 24 cm.

The side of the parallelogram is two times greater than the adjacent side (AB>AD).

CE is the height of the side AB

The area of the parallelogram is 24 cm².

Find the height of CE

Video Solution

Step-by-Step Solution

The perimeter of the parallelogram is calculated as follows:

$S_{ABCD}=AB+BC+CD+DA$ Since ABCD is a parallelogram, each pair of opposite sides is equal, and therefore, AB=DC and AD=BC

According to the figure that the side of the parallelogram is 2 times larger than the side adjacent to it, it can be argued that $AB=DC=2BC$

We inut the data we know in the formula to calculate the perimeter:

$P_{ABCD}=2BC+BC+2BC+BC$

We replace the given perimeter in the formula and add up all the BC coefficients accordingly:

$24=6BC$

We divide the two sections by 6

$24:6=6BC:6$

$BC=4$

We know that $AB=DC=2BC$ We replace the data we obtained (BC=4)

$AB=DC=2\times4=8$

As ABCD is a parallelogram, then all pairs of opposite sides are equal, therefore BC=AD=4

To find EC we use the formula: $A_{ABCD}=AB\times EC$

We replace the existing data:

$24=8\times EC$

We divide the two sections by 8 $24:8=8EC:8$

$3=EC$

Answer

3 cm

Question 1

ABCD is a parallelogram whose perimeter is equal to 22 cm.

AC=4 height of the parallelogram for side CD is 3 cm

Calculate the area of the parallelogram

Question 2

Calculate the perimeter of the parallelogram ABCD.

AB is parallel to CD.

Question 3

A parallelogram is shown below.

AB = 5

AC = 2X

The perimeter of the parallelogram is 20.

Calculate the length of side AC.

Question 4

A parallelogram is shown below.

AB = 8

AC = X+2

The perimeter of the parallelogram is 30.

Calculate X.

Question 5

Below is a parallelogram.

AB = 4

AC = X-2

The perimeter of the parallelogram is 10.

Calculate X.

Exercise #6

ABCD is a parallelogram whose perimeter is equal to 22 cm.

AC=4 height of the parallelogram for side CD is 3 cm

Calculate the area of the parallelogram

Video Solution

Answer

21 cm².

Exercise #7

Calculate the perimeter of the parallelogram ABCD.

AB is parallel to CD.

Video Solution

Answer

$2x+20$

Exercise #8

A parallelogram is shown below.

AB = 5

AC = 2X

The perimeter of the parallelogram is 20.

Calculate the length of side AC.

Video Solution

Answer

Exercise #9

A parallelogram is shown below.

AB = 8

AC = X+2

The perimeter of the parallelogram is 30.

Calculate X.

Video Solution

Answer

Exercise #10

Below is a parallelogram.

AB = 4

AC = X-2

The perimeter of the parallelogram is 10.

Calculate X.

Video Solution

Answer

Question 1

Given a parallelogram in which the length of one side is 2 greater than the length of another side and given that the length of the larger side is 2X:

Express by X the perimeter of the parallelogram.

Question 2

Given a parallelogram in which the length of one side is 2 times the length of the other side and given that the length of the larger side is 0.5X:

Express by X the perimeter of the parallelogram.

Question 3

Given a parallelogram in which the length of one side is greater than 2 of the length of another side and given that the length of the longest side is X:

Express by X the perimeter of the parallelogram.

Question 4

Given a parallelogram where the length of one side is greater by 4 than the length of another side and given that the length of the smaller side is X:

Express by X the perimeter of the parallelogram.

Question 5

How long is side BC given that the perimeter of the parallelogram is 30 cm?

$$ CD=2x $$

Exercise #11

Given a parallelogram in which the length of one side is 2 greater than the length of another side and given that the length of the larger side is 2X:

Express by X the perimeter of the parallelogram.

Video Solution

Answer

Exercise #12

Given a parallelogram in which the length of one side is 2 times the length of the other side and given that the length of the larger side is 0.5X:

Express by X the perimeter of the parallelogram.

Video Solution

Answer

1.5X

Exercise #13

Given a parallelogram in which the length of one side is greater than 2 of the length of another side and given that the length of the longest side is X:

Express by X the perimeter of the parallelogram.

Video Solution

Answer

Exercise #14

Given a parallelogram where the length of one side is greater by 4 than the length of another side and given that the length of the smaller side is X:

Express by X the perimeter of the parallelogram.

Video Solution

Answer

4X+8

Exercise #15

How long is side BC given that the perimeter of the parallelogram is 30 cm?

$CD=2x$

Video Solution

Answer

$15-2x$

Question 1

Look at the parallelogram below.

AB = 10

AC = X

The perimeter of the parallelogram is 30.

Calculate X.

Question 2

Shown below is a parallelogram.

AB = 7

AC = 0.5X

The perimeter of the parallelogram is 21.

Calculate side AC.

Question 3

ABCD is a parallelogram whose perimeter is equal to 22 cm.

Side AB is smaller by 5 than side AD

The height of the parallelogram for the side AD is 2 cm

What is the area of the parallelogram?

Exercise #16

Look at the parallelogram below.

AB = 10

AC = X

The perimeter of the parallelogram is 30.

Calculate X.

Video Solution

Answer

Exercise #17

Shown below is a parallelogram.

AB = 7

AC = 0.5X

The perimeter of the parallelogram is 21.

Calculate side AC.

Video Solution

Answer

3.5

Exercise #18

ABCD is a parallelogram whose perimeter is equal to 22 cm.

Side AB is smaller by 5 than side AD

The height of the parallelogram for the side AD is 2 cm

What is the area of the parallelogram?

Video Solution

Answer

16 cm²