Question

The length of a rectangle is 12 m more than twice the width. The area of the rectangle is 320
square m. Write an equation that can be used to find the length and width of the rectangle. Also
find the dimensions of the rectangle.

Answer 1

Let length of the rectangle be 'x'm and width be 'y'm.
Hence, x=2y+12
Also, xy=320
From both the equations,
(2y+12)y=320
2y²+12y=320
2y²+12y-320=0
2y²-20y+32y-320=0
2y(y-10)+32(y-10)=0
(2y+32)(y-10)=0
Either 2y+32=0
2y=-32
y=-16
This is not possible as the dimensions should be positive.
Hence, y-10=0
y=10
Substituting the value of y in the equation,
xy=320
10x=320
x=32
Length of rectangle=32m
Breadth of rectangle= 10m.