Question

A fence is guarding off a vegetable garden in the form of a rectangle. It has one side that is 10m greater than the other side. Find the length of the fence needed to surround this garden if the area of the vegetable garden is 2184m2.'

Answer 1

188

Step-by-step explanation:

Let the width be represented by x

Since length is 10 m more than the width, the length is (x+10) m

The area is given by product of length by width

x(x+10)=2184

`x^(2)+10x=2184`

`x^(2)+10x-2184=0`

By factorization, two numbers whose product is -2184 and their sum is 10 are 52 and -42

x(x-42)+x(x+52)=0

x=42 or -52

Since width can't be a negative number, x=42 m

Length=x+10=42+10=52

Perimeter=2(l+w)=2(52+42)=188 m