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∆ABC is similar to ∆DEF. The perimeter of ∆ABC is five times the perimeter of ∆DEF. The area of ∆ABC is 100 square centimeters. The area of ∆DEF is square centimeters. NextReset

User AlphaOmega
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2 Answers

4 votes

Answer:

4 square centimeters

Explanation:

User Nathan Hughes
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8.4k points
6 votes

Answer:

The area of ∆DEF is 4 square centimeters.

Explanation:

Given ∆ABC is similar to ∆DEF.

The perimeter of ∆ABC is five times the perimeter of ∆DEF. It means:-

(perimeter of ΔABC) = 5 times (perimeter of ΔDEF)

(perimeter of ΔABC) / (perimeter of ΔDEF) = 5

It means Scale factor, K = 5.

Given The area of ∆ABC is 100 square centimeters.

(area of ∆ABC) / (area of ∆DEF) = k²

100 / (area of ∆DEF) = 5² = 25.

(area of ∆DEF) = 100 / 25 = 4.

Hence, The area of ∆DEF is 4 square centimeters.

User JsNgian
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9.2k points
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