find the dimensions of the original rectangle

Question

a rectangle has a length of 8 m less than twice its width. when 2 m are added to the width, the resulting figure is a square with an area of 144 m^2. 

Answer 1

Let W = original width

 

then 2W - 8 = length

 

When 2 is added to the width (W + 2), the figure becomes a square.

 

Area of a square = side²             Now write an equation

 

144 = (W + 2)²                         multiply (W + 2)(W + 2)

 

144 = W² + 4W + 4                  set equal to zero by subtracting 144 from both sides

 

    0 = W² + 4W - 140               factor the quadratic      -140 = 14(-10) 

 

    0 = (W +14)(W - 10)            set each factor equal to zero and solve each

 

W + 14 = 0        W - 10 =  0

 

       W = -14            W = 10m  This is the original width

 

Since we are dealing with the dimensions of a rectangle the value can't be negative.  We eliminate the -14

 

CHECK

 

If we add 2 to the original width of 10 we get 12.  If a square has a side of 12m then the area of the square

would be 144m²  √

 

 

Answer 2

Original rectangle:

 

width = x

length = 2x - 8

 

 

Add 2 m to the width to get a square.  A square has equal sides all around.

 

width = x + 2

length = x + 2

Area = 144 m²

 

 

Write an equation that represents the area of a square.

 

(x + 2)(x + 2) = 144

 

 

Solve for x.

 

(x + 2)² = 144

 

x + 2 = 12

 

x = 10

 

 

Plug in this value of x to find the length of the original rectangle.

 

width = 10 m

length = 12 m