Perimeter of a Rectangle: Using variables

Look at the following rectangle:

The area of the rectangle is 20.

What is the perimeter of rectangle ABCD?

The area of the rectangle equals length multiplied by width:

$S=AB\times AD$

Let's substitute the data into the formula:

$20=4\times(x+1)$

$20=4x+4$

$20-4=4x$

$16=4x$

$4=x$

Now we can calculate side AB:

$4+1=5$

The perimeter of the rectangle equals the sum of all sides together

Since in a rectangle each pair of opposite sides are equal, we can state that:

$AD=BC=4$

$AB=CD=5$

Now let's add all the sides together to find the perimeter:

$4+5+4+5=8+10=18$

18

Look at the following rectangle:

The perimeter of the rectangle is 26.

Calculate the value of X.

Since in a rectangle every pair of opposite sides are equal, we can claim that:

$AD=BC=x+2$

$AB=CD=x+3$

Since the perimeter of the rectangle is equal to 26, we can substitute the data into the formula:

$26=x+2+x+3+x+2+x+3$

$26=4x+10$

$26-10=4x$

$16=4x$

Let's divide both sides by 4:

$4=x$

4

Look at the following rectangle:

The perimeter of the rectangle is 20.

Calculate the value of X.

Since in a rectangle every pair of opposite sides are equal, we can claim that:

$AD=BC=2x+1$

$AB=CD=4x+3$

Since the perimeter of the rectangle is equal to 20, we can substitute the data into the formula:

$20=2x+1+4x+3+2x+1+4x+3$

$20=12x+8$

$20-8=12x$

$12=12x$

Let's divide both sides by 12:

$1=x$

$1$

Look at the following rectangle:

Given that the area of the triangle ABD is 9, what is the perimeter of the rectangle ABCD?

Area of triangle ADB:

$\frac{AD\times AB}{2}$

Let's list the known data:

$9=\frac{x+2\times6}{2}$

$9=(x+2)\times3$

$9=3x+6$

$9-6=3x$

$3=3x$

$1=x$

Side AD equals:

$1+2=3$

Since in a rectangle, each pair of opposite sides are equal, we can state that:

$AD=BC=3$

$AB=CD=6$

Now we can calculate the perimeter of the rectangle:

$3+6+3+6=6+12=18$

18

Look at the following rectangle:

Given that the perimeter of the triangle BCD is 20, what is the perimeter of the rectangle ABCD?

Given that the perimeter of triangle BCD is 20

We can therefore insert the existing data and calculate as follows:

$20=10+6+x+2$

$20=16+x+2$

$20-16-2=x$

$x=2$

Now we can calculate the BC side: 2+2=4

Perimeter of the rectangle ABCD:

$6+6+4+4=12+8=20$

20

The rectangle in the diagram is composed of of three smaller rectangles.

Calculate x given that GDEF has a perimeter of 44.

Let's calculate the perimeter of rectangle GDEF using the given data:

$10x-8+10x-8+5x+5x=44$

We'll group similar terms:

$30x-16=44$

$30x=44+16$

$30x=60$

$x=2$

2

The area of the square whose side length is 4 cm is
equal to the area of the rectangle whose length of one of its sides is 1 cm.

What is the perimeter of the rectangle?

After squaring all sides, we can calculate the area as follows:

$4^2=16$

Since we are given that the area of the square equals the area of the rectangle , we will write an equation with an unknown since we are only given one side length of the parallelogram:

$16=1\times x$

$x=16$

In other words, we now know that the length and width of the rectangle are 16 and 1, and we can calculate the perimeter of the rectangle as follows:

$1+16+1+16=32+2=34$

34

Given the following rectangle:

The perimeter of the rectangle is 32.

Find the value of the parameter x.

3

The perimeter of the rectangle below is 36.

Calculate the value of x.

4

The rectangle below is composed of two rectangles.

Calculate the value of the x, given that the perimeter of the rectangle is 48.

2

The perimeter of the rectangle below is 28.

Calculate the value of x.

3

The perimeter of the rectangle below is 12.

Calculate x.

2

The perimeter of the rectangle below is 8.

Calculate x.

1

The perimeter of the rectangle below is 24.

Calculate x.

6

The rectangle below is composed of two smaller rectangles.

Calculate x given that the perimeter of rectangle ABCD is 48.

4

The rectangle below is composed of two smaller rectangles.

Calculate x given that the perimeter of rectangle AEFD is 30.

2

The rectangle below is composed of two smaller rectangles.

Calculate x given that the perimeter of rectangle ABCD is 42.

4

Look at the following rectangle:

The area of the rectangle is 7.

What is the perimeter of the rectangle?

16

The shape below is composed of three rectangles.

Calculate x given that the perimeter of rectangle GCHF is 18.

1

The shape below is composed of three rectangles.

Calculate x given that the perimeter of rectangle ABHF is 52.

3