# The area of a rectangular room is 65m2. Find the perimeter of the room given that its length is 3m more than thrice its width.

1## Answers

The area of a rectangle is given by the formula: A = lw

Given that its length is 3m more than thrice its width you'll have:

l = 3w + 3 -----equation1

and

A = 65m²

Substitute everything to the area formula you'll have:

A = lw65m² = (3w + 3 ) (w)

65 = 3w² + 3w or

3w² + 3w - 65 = 0

using quadratic formula you'll have:

take the positive value since there's no negative length.

__w = 4.1815m__

substitute to equation 1

l = 3w + 3

l = 3(4.1815) + 3

__l = 15.5445m__

__Since you are asked of the perimeter then you'll have the formula for perimeter of a rectangle used. __

P = 2l + 2w

Substituting you'll have:

P = 2 (15.5445) + 2(4.1815)

__P = 39.452meters__