Solving Equations Using All Methods: Using additional geometric shapes

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

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

Let's set up the data in the formula:

$27=3x\times x$

$27=3x^2$

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

$9=x^2$

$x=\sqrt{9}=3$

$x=3$

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

Calculate x.

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

$x=36$

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.

$x=2$

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

Calculate x.

$x=4$

The area of a square 49 cm².

Calculate the side length of the square.

$x=7$

Look at triangle ABC below.

$∢A+∢B=2∢C$

$∢B=3∢A$

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

60°

$∢B$ is 2 times bigger than $∢A$ and$∢C$ is 3 times bigger than $∢B$.

Calculate $∢A$.

20°

The triangle ABC is shown below.

angle $∢A=70°$.

$\frac{∢B}{∢C}=\frac{1}{3}$

Calculate angle $∢C$.

82.5°

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

Calculate X.

$x=2$