Solving an Equation by Multiplication/ Division: Using additional geometric shapes

Question 1

The area of the rectangle below is equal to 22x.

Calculate x.

Question 2

Given: the length of a rectangle is 3 greater than its width.

The area of the rectangle is equal to 27 cm².

Calculate the length of the rectangle

Question 3

The perimeter of the triangle ABC is equal to 17 cm.

Calculate X.

Question 4

Is it possible to calculate X? If so, what is it?

Question 5

Given: the area of the triangle is equal to 2 cm² and the height of the triangle is 4 times greater than its base.

The area of the trapezoid is equal to 12 cm² (use x)

Calculate the value of x.

Examples with solutions for Solving an Equation by Multiplication/ Division: Using additional geometric shapes

Exercise #1

The area of the rectangle below is equal to 22x.

Calculate x.

Video Solution

Step-by-Step Solution

The area of the rectangle is equal to the length multiplied by the width.

Let's list the known data:

$22x=\frac{1}{2}x\times(x+8)$

$22x=\frac{1}{2}x^2+\frac{1}{2}x8$

$22x=\frac{1}{2}x^2+4x$

$0=\frac{1}{2}x^2+4x-22x$

$0=\frac{1}{2}x^2-18x$

$0=\frac{1}{2}x(x-36)$

For the equation to be equal, x needs to be equal to 36

Answer

$x=36$

Exercise #2

Given: the length of a rectangle is 3 greater than its width.

The area of the rectangle is equal to 27 cm².

Calculate the length of the rectangle

Video Solution

Step-by-Step Solution

The area of the rectangle is equal to length multiplied by width.

Let's set up the data in the formula:

$27=3x\times x$

$27=3x^2$

$\frac{27}{3}=\frac{3x^2}{3}$

$9=x^2$

$x=\sqrt{9}=3$

Answer

$x=3$

Exercise #3

The perimeter of the triangle ABC is equal to 17 cm.

Calculate X.

Video Solution

Answer

Exercise #4

Is it possible to calculate X? If so, what is it?

Video Solution

Answer

Impossible

Exercise #5

Given: the area of the triangle is equal to 2 cm² and the height of the triangle is 4 times greater than its base.

The area of the trapezoid is equal to 12 cm² (use x)

Calculate the value of x.

Video Solution

Answer

$x=2$

Question 1

Is it possible to calculate X? If so, what is it?

Question 2

Is it possible to calculate X? If so, what is it?

Question 3

Below is a deltoid with a length 2 times its width and an area equal to 16 cm².

Calculate x.

Question 4

The area of a square 49 cm².

Calculate the side length of the square.

Question 5

The area of the triangle below is equal to 10 cm² and its height is 5 times greater than its base.

Calculate X.

Exercise #6

Is it possible to calculate X? If so, what is it?

Video Solution

Answer

$9$

Exercise #7

Is it possible to calculate X? If so, what is it?

Video Solution

Answer

$14.5$

Exercise #8

Below is a deltoid with a length 2 times its width and an area equal to 16 cm².

Calculate x.

Video Solution

Answer

$x=4$

Exercise #9

The area of a square 49 cm².

Calculate the side length of the square.

Video Solution

Answer

$x=7$

Exercise #10

The area of the triangle below is equal to 10 cm² and its height is 5 times greater than its base.

Calculate X.

Video Solution

Answer

$x=2$

Question 1

Look at triangle ABC below.

$$ ∢A+∢B=2∢C $$

$$ ∢B=3∢A $$

Calculate the size of angle $\sphericalangle C\text{.}$

Question 2

A pentagonal figure, two of its sides are equal and the length of each is 8 cm, the other three sides are equal to each other.

The perimeter of the pentagon is equal to 31 cm, write an equation based on the data and determine the unknown

Exercise #11

Look at triangle ABC below.

$∢A+∢B=2∢C$

$∢B=3∢A$

Calculate the size of angle $\sphericalangle C\text{.}$

Video Solution

Answer

60°

Exercise #12

A pentagonal figure, two of its sides are equal and the length of each is 8 cm, the other three sides are equal to each other.

The perimeter of the pentagon is equal to 31 cm, write an equation based on the data and determine the unknown

Video Solution

Answer

$x=5$