MATH SOLVE

7 months ago

Q:
# 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.

Accepted Solution

A:

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

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