Question

The perimeter of a rectangular parking lot is 94 meters. The area is 540 square meters. What are the dimensions of the parking lot?

Answer 1

Hi,

27,20

Explanation:

Let's assume a the length and b the width of the parking.

`\left\{\begin{array}{ccc}2*(a+b)&=&94\\a*b&=&540\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}b&=&47-a\\a*(47-a)&=&540\\\end {array} \right.\\\\\\a*(47-a)=540\\a^2-47a+540=0\\\Delta=47^2-4*540=49=7^2\\\\a=(47+7)/(2) \ or\ a=(47-7)/(2) \\\\a=27\ or\ a=20\\\\\left\{\begin{array}{ccc}a&=&27\\b&=&47-27\\\end {array} \right.\ or\ \left\{\begin{array}{ccc}a&=&20\\b&=&47-20\\\end {array} \right.\\\\`

The dimensions of the parking are length=27 and wide=20 (because a length is greater or equal to the width)