Area of a triangle PQR right-angled at Q is 60 $cm 2$ as shown in the figure below. If the smallest side is 8cm long, then the length of the sides QR and PR are

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15, 17

16,15

15,11

17,15

answer is A.

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Detailed Solution

Given, area of a triangle PQR right-angled at Q = 60

cm 2

.
The smallest side length = 8 cm.
We know that the area of a triangle is half the product of base length and height or altitude.
So, using the formula for the area of a triangle, we have,

A r (Δ PQR) = 12 × base × height

60 = 12 × PQ × QR 60 = 12 × 8 × QR QR = 60 × 2 8 QR = 15 cm

So, the altitude QR of the given right-angled triangle is obtained as 15 cm.
Now, we need to find the length of the hypotenuse PR.
So, applying the Pythagoras theorem on triangle PQR, we get,

P R 2 = 82 + 152 P R 2 = 64 + 225 P R 2 = 289 P R = 289 P R = 17

So, the length of the hypotenuse PR is obtained as 17 cm.
Therefore, the lengths of the other two sides of the given right-angled triangle viz., QR and PR are obtained as 15 cm and 17 cm respectively. Hence, the correct option is 1.

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