Question

The width of a rectangle is 4cm less than the length. If each dimension were increased by 3cm, the width of the new rectangle formed would be 2/3 the length of the new rectangle. Find the dimensions of the original rectangle.

Answer 1

The original length is 9 cm and the original width 5 cm

Explanation:

The area of a rectangle A is given as the product of its' length L and width W.

Given that the width of a rectangle is 4cm less than the length then

W = L - 4

If each dimension were increased by 3cm, then the new

Length

= L + 3

Width

= W + 3

the width of the new rectangle formed would be 2/3 the length of the new rectangle

W + 3 = 2/3(L + 3)

3W + 9 = 2L + 6

3W = 2L +6 - 9

3W = 2L - 3

Recall that W = L - 4

3(L - 4) = 2L - 3

3L - 12 = 2L - 3

3L - 2L = 12 - 3

L = 9 cm

W = 9 - 4

= 5 cm