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Q.

Area of a right-angled triangle is 30 $cm 2$ . If its smallest side is 5 cm, then its hypotenuse is:

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a

14 cm

b

13 cm

c

12 cm

d

11cm

answer is B.

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Detailed Solution

Given, area of a right-angled triangle =30

cm 2

.
The smallest side length = 5 cm.
We know that the area of a triangle is half the product of its base length and its altitude.
Let the smallest side (base) be say ‘b,’ given as 5 cm and height be say ‘h’.
So,

12 × 5 × h = 30 h = 30 × 2 5 h = 6 × 2 h = 12 cm

Therefore, the height of the right-angled triangle is obtained as 12 cm.
Now, let us assume the hypotenuse of the triangle as ‘H’.
So, by Pythagoras theorem, we have,

H = b 2 + h 2 52 + 122 = 25 + 144 = 169 = 13 cm

So, the hypotenuse of the right-angled triangle is obtained as 13 cm.
Hence, the correct option is (2).

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