Answer:
[tex]Height = 15[/tex]
[tex]Base = 45[/tex]
Step-by-step explanation:
Given
Shape: Rectangle
[tex]Perimeter = 120cm[/tex]
[tex]Base = 3 * Height[/tex]
Required
Determine the dimensions
The perimeter of a rectangle is:
[tex]Perimeter = 2 * (Base + Height)[/tex]
Substitute 120 for Perimeter
[tex]120 = 2 * (Base + Height)[/tex]
Divide both sides by 2
[tex]60 = Base + Height[/tex]
Substitute 3 * Height for Base
[tex]60 = 3 * Height + Height[/tex]
[tex]60 = 3Height + Height[/tex]
[tex]60 = 4Height[/tex]
Divide both sides by 4
[tex]15 = Height[/tex]
[tex]Height = 15[/tex]
Substitute 15 for Height in [tex]Base = 3 * Height[/tex]
[tex]Base = 3 * 15[/tex]
[tex]Base = 45[/tex]
