Question

A rectangle is twice as long as it is wide. if its length is increased by 4 cm and its width is decreased by 3 cm, the new rectangle formed has an area of 100 cm2. find the dimensions of the original rectangle.

Answer 1

Original Rectangle:
long: L = 2W
Width: W
New rectangle:
long: L = 2W + 4
Width: W - 3
Area: 100
We have then:
A = (2W + 4) * (W-3)
Rewriting:
A = 2W ^ 2 - 6W + 4W - 12
A = 2W ^ 2 - 2W - 12
Substituting the area:
2W ^ 2 - 2W - 12 = 100
Rewriting:
2W ^ 2 - 2W - 112 = 0
Which roots are:
W = -7
W = 8
Taking the positive root, we look for the dimension of the original triangle:
L = 2W = 2 (8) = 16
Answer:
The dimensions of the original rectangle are:
W = 8 cm
L = 16 cm