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

Answer:

$Height = 15$

$Base = 45$

Step-by-step 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 $Base = 3 * Height$

$Base = 3 * 15$

$Base = 45$