Two corresponding sides of two similar triangles are 3 cm and 5 cm. The area of the first triangle is 12 cm. What is the area of the second triangle?

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01-06-2022
Mathematics

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Two corresponding sides of two similar triangles are 3 cm and 5 cm. The area of the first triangle is 12 cm. What is the area of the second triangle?

Sagot :

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oladayoademosu oladayoademosu · Answer 1 · 2022-06-07T09:55:22-04:00

Since the are of the first triangle is 12 cm², the area of the second triangle is 33.33 cm².

To answer the question, we need to know what similar triangles are

What are similar triangles?

Similar triangles are triangles in which the ratio of their corresponding sides is constant.

Given that the corresponding sides of the two similar triangles are 3 cm and 5 cm respectively. Also, the area of the first triangle is 12 cm². We need to find the area of the second triangle.

Area of second triangle

Since the triangles are similar, we have that

(side of second triangle/side of first triangle)² = Area of second triangle/Area of first triangle

Area of second triangle = (side of second triangle/side of first triangle)² × Area of first triangle

= (5 cm/3 cm)² × 12 cm²

= 25/9 × 12 cm²

= 25/3 × 4 cm²

= 100 cm²/3

= 33.33 cm²

So, the area of the second triangle is 33.33 cm².

Learn more about similar triangles here:

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Sagot :

What are similar triangles?

Area of second triangle

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