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The perimeters of two similar triangles ABC and PQR are respectively 36 cm and 24 cm. If PQ = 10 cm, find AB - Mathematics

Sum

The perimeters of two similar triangles ABC and PQR are respectively 36 cm and 24 cm. If PQ = 10 cm, find AB

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Solution

Since the ratio of the corresponding sides of similar triangles is same as the ratio of their perimeters.

∴ ∆ABC ~ ∆PQR

`\Rightarrow \frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}=\frac{36}{24}`

`\Rightarrow \frac{AB}{PQ}=\frac{36}{24}\Rightarrow\frac{AB}{10}=\frac{36}{24}`

`\Rightarrow AB=\frac{36\times 10}{24}cm=15cm`

Concept: Similarity
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