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

Exercises on Both Sides (of the Equation)Combining like terms Binomial Number of terms Decimal numbers Rearranging Equations Using fractions Solving an equation using all techniques One sided equations Solving an equation with fractions Equations with variables on both sides Addition, subtraction, multiplication and division

Question 1

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 2

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

Calculate $$ x $$ .

Question 3

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.

Question 4

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

Question 5

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

Calculate x.

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

Exercise #1

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 #2

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

Calculate $x$ .

Video Solution

Step-by-Step Solution

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

Let's write out 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 balanced, $x$ needs to be equal to 36.

Answer

$x=36$

Exercise #3

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

$x=2$

Exercise #4

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

Video Solution

Answer

Impossible

Exercise #5

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

Calculate x.

Video Solution

Answer

$x=4$

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

The area of a square 49 cm².

Calculate the side length of the square.

Question 4

Look at triangle ABC below.

$$ ∢A+∢B=2∢C $$

$$ ∢B=3∢A $$

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

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

The area of a square 49 cm².

Calculate the side length of the square.

Video Solution

Answer

$x=7$

Exercise #9

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 #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

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

Calculate X.

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

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

Calculate X.

Video Solution

Answer

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

$x=5$