Two similar rectangles have a scale factor of 3:2. The perimeter of the small rectangle is 50 feet. What is the perimeter of the large rectangle measured in feet?

[tex]\dfrac{\text{perimeter of large rectangle}}{\text{perimeter of small rectangle}}=\dfrac{3}{2}\\\\\Rightarrow\ \dfrac{\text{perimeter of large rectangle}}{50}=\dfrac{3}{2}\\\\\Rightarrow\ \text{Perimeter of large rectangle} =\dfrac{3}{2}\times50\\\\\Rightarrow\ \text{Perimeter of large rectangle} =75[/tex]

Hence, the perimeter of the large rectangle measured 75 feet.

MrRoyal MrRoyal · Answer 2 · 2022-01-18T11:19:09+01:00

The perimeter of a rectangle is the sum of the dimension of the rectangle

The perimeter of the larger rectangle is 75 feet

The ratio of the side length is given as:

[tex]Ratio = 3 : 2[/tex]

Represent the perimeters of both rectangles with

P1 and P2.

So, we have:

[tex]P1 : P2 = 3 : 2[/tex]

The smaller rectangle has a perimeter of 50 feet.

So, we have:

[tex]P1 : 50 = 3 : 2[/tex]

Express as fraction

[tex]\frac{P1 }{ 50 }= \frac 3 2[/tex]

Multiply both sides by 50

[tex]P1= \frac 3 2 \times 50[/tex]

[tex]P1= 75[/tex]

Hence, the perimeter of the larger rectangle is 75 feet