Question

The perimeter of a rectangle is 120 centimeters. The base is 3 times the height. What are the dimensions of the rectangle? a. h = 9cm, b = 18 cm c. h = 15 cm, b = 45 cm b. h = 19 cm, b = 57 cm d. h = 10 cm, b = 15 cm

Answer 1

`Height = 15`

`Base = 45`

Explanation:

Given

Shape: Rectangle

`Perimeter = 120cm`

`Base = 3 * Height`

Required

Determine the dimensions

The perimeter of a rectangle is:

`Perimeter = 2 * (Base + Height)`

Substitute 120 for Perimeter

`120 = 2 * (Base + Height)`

Divide both sides by 2

`60 = Base + Height`

Substitute 3 * Height for Base

`60 = 3 * Height + Height`

`60 = 3Height + Height`

`60 = 4Height`

Divide both sides by 4

`15 = Height`

`Height = 15`

Substitute 15 for Height in
`Base = 3 * Height`

`Base = 3 * 15`

`Base = 45`