The ratio of corresponding side lengths are 1:3. the perimeter of the smaller triangle is 36 inches. the area of the smaller triangle is 54 square inches. What is the perimeter and area of the larger figure?

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The ratio of corresponding side lengths are 1:3. the perimeter of the smaller triangle is 36 inches. the area of the smaller triangle is 54 square inches. What is the perimeter and area of the larger figure?

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Answer 1 · 2017-07-16T21:05:04

See explanation.

Explanation:

The ratio of the side lengths is $1 : 3$ $1:3$ , so all sides of the larger triangle are 3 times larger than the sides of the smaller one. Therfore the perimeter of the larger triangle is also 3 times larger. It is: $3 \times 36 = 108$ $3xx36=108$ inches.

There is a theorem which says:

The ratio of areas of a similar figures equals the square of the ratio of the similarity.

In the example the ratio of the similarity is $3$ $3$ , therfore the larger triangle has $3^{2} = 9$ $3^2=9$ times larger area:

$A_{2} = 9 \times A_{1} = 9 \times 54 = 486$ $A_2=9xxA_1=9xx54=486$ square inches

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The ratio of corresponding side lengths are 1:3. the perimeter of the smaller triangle is 36 inches. the area of the smaller triangle is 54 square inches. What is the perimeter and area of the larger figure?

1 Answer

Explanation:

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