A green rectangular tile and a yellow rectangular tile are similar. The green tile has a length of 24 centimeters and a perimeter of 80 centimeters. The yellow tile has a length of 72 centimeters. What is the perimeter of the yellow tile?

Question

Mathematics

Gunnar Medina

2 March, 13:27

A green rectangular tile and a yellow rectangular tile are similar. The green tile has a length of 24 centimeters and a perimeter of 80 centimeters. The yellow tile has a length of 72 centimeters. What is the perimeter of the yellow tile?

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Answers (1)

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Ally Norton · Answer 1

Answer: The perimeter of the yellow rectangular tile is 240 centimeters.

Explanation: To find the answer, write this information as a proportion since we know that the rectangles are similar.

(Assume that in both ratios, the numerator is the length of the rectangle, and the denomiator is the perimeter. Also, the left side is for the green rectangle and the right side is for the yellow rectangle.)

Since we don't know the perimeter of the yellow rectangle, let's express it as x.

24/80 = 72/x

A good shortcut is to cross multiply. To do this, multiply the left numerator by the right denominator, and the left denominator by the right numerator, and set both products equal to each other.

24 • x = 80 • 72

Simplify the equation.

24x = 5760

Divide both sides by 24.

x = 240

Since x = 240, we know that the perimeter of the yellow rectangular tile is 240 centimeters.