A triangle ABC is similar to a triangle PQR. If the triangle ABC has sides with ratio of 3:4:5 and the shortest side of the triangle PQR is 6 cm, then find the length of the longest side of the triangle PQR.

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Solution

The correct option is D 10
Given that the triangles ABC and PQR are similar. If two triangles are similar, the lengths of their sides are proprtional.

In the triangle ABC, sides are in the ratio $3 : 4 : 5$ .

Let the two unknown sides of trianlge PQR be $x$ and $y$ .
Ratio of lengths of the sides of the triangle PQR is $6 : x : y$ .
$3 : 4 : 5 = 6 : x : y \Rightarrow x = 8, y = 10$

So, the longest side of the triangle PQR is 10 cm in length.

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