The length of a rectangular piece of land is 5m more than twice the width. Given that the land area is 168m², what is the perimeter of the land?

Answer 1

Hi Sarah

The Perimeter is 58 m

Given

Length = 2w + 5

Width = w

Area = Width x Length

168 = w(2w + 5)

168 = 2w² + 5w

We can set up a quadratic by subtracting 168 from both sides of the equation

0 = 2w² + 5w - 168

Next we factor by using factors of 168 and 2 that combine in such a way to yield a positive 5

I came up with

0 = (2w + 21)(w - 8)

w cannot be negative so

w = 8

L = 2(8) + 5

L = 16 + 5

L = 21

Perimeter = 2(Length) + 2(Width) = 2(L) + 2(w) = 2(21) + 2(8) = 42 + 16 = 58

You can check the numbers as follows

Area = Length x Width = 21 x 8 = 168

I hope you find this useful email me if you have any questions