Lesson 5.2.3
Step 1 – Write the Equation for rectangle
Solve for X

Length = x
Width = (x-1)
Area = 20

Equation for area of Rectangle = L * W = Area
Since L = x and W = (x-1) and Area = 20
Then it is “x(x-1) = 20”

Step 2 – Distribute

x(x)-x(1) = 20
x^2 – x = 20

Step 3 – Write in standard form

Because you can not solve for x by simply adding x to the other side, you must take the 22 to the x’s side
x^2 – x – 20 = 0
From here you can factor

Step 4 – Factor

(x – 5)(x + 4) = 0

Step 5 – Solve

x – 5 = 0
x = 5

x + 4 = 0
x = -4

Because you can not have a negative length in a rectangle, the answer is
5

Step 1 – Write equation for triangle

Base = x
Height = x
Area = 38

Equation for area of triangle = (B * H)/2 = Area
Since B = x and Height = x and area = 38
Then it is “[x(x)]/2 = 38”

Step 2 – Simplify and distribute

Because the “/2” is a hassle, we will get rid of it by multiplying 2 to the other side to cancel the 2.
2[x(x)]/2 = 38 * 2
x(x) = 64
x(x) + x = 64
x^2 + x = 64

Step 3 – Write in standard form

Since it is more difficult to solve by subtracting the 8x to the other side, we shall take the 64 to the x’s side side.
x^2 + x – 64
From here you can factor

Step 4 – Factor

(x+8)(x-8)

Step 5 – Solve

X + 8 = 0
X= -8

X – 8 = 0
X = 8

Since you can not have a negative length, the answer is
58

NOW YOU TRY!

1.) Rectangle
Length = (x + 6)
Width = x
Area = 16

2.) Triangle
Base = 2x
Height = (x + 1)
Area = 0