A rectangle has a perimeter if 46 cm and an area of 120 cm^2. How do you find its dimensions by writing an equation and using the quadratic formula to solve it?

1 Answer
Apr 7, 2018

The dimensions are 8 cm and 15 cm.

Explanation:

Let the length be xx and the width be yy

The perimeter of the rectangle is 2x+2y2x+2y

The area of the rectangle is xyxy

We now have two equations,

2x+2y=46 or x+y=232x+2y=46orx+y=23 we’ll call this equation (1)

And xy=120xy=120 equation (2)

From (2), y=120/xy=120x, substitute this into (1)

therefore x+120/x=23

x^2+120=23x multiply both sides by x

x^2-23x+120=0 subtract 23x from both sides

(x-8)(x-15)=0 factorise

x=8 or 15 solve linear equations

From (2), when x=8, 8y=120=>y=15

When x=15, 15y=120=>y=8

therefore the dimensions are 8 cm and 15 cm.