Question

The area of a rectangle is 192 in squared. The ratio of the length to the width is 4 : 3. Find the length and the width.

Answer 1

Answer: L = 16 inches , W = 12 inches

Explanation:

Area = 192
`in^(2)`

Ratio of length to the width = 4 : 3

This means that L =
`(4)/(3)` W

Area of a rectangle = Length x width

Substituting A = 192 and L =
`(4)/(3)` W into the formula for calculating area of rectangle , we have

192 =
`(4)/(3)` W x W

192 =
`(4W^(2) )/(y)`

192 X 3 =
`4W^(2)`

576 =
`4W^(2)`

Divide through by 4

144 =
`W^(2)`

Take the square root of both sides

Therefore :

W = 12 inches

Substitute W = 12 into L = 4/3W , which means

L = 4/3 X 12

L = 16 inches

Therefore :

Length = 16 inches and Width = 12 inches