JEE Advance - Mathematics (2017 - Paper 1 Offline - No. 9)
The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its smallest side?
Answer
6
Explanation
Let the sides be given by a $$-$$ d, a, a + d, where (a, d > 0). Also, d < a.
By the condition,
a2 + (a $$-$$ d)2 = (a + d)2
$$\Rightarrow$$ a2 = (a + d)2 $$-$$ (a $$-$$ d)2
$$\Rightarrow$$ a2 = 4ad $$\therefore$$ a = 4d
Thus the sides are 3d, 4d, 5d.
As area = 24, we have $${1 \over 2}$$ . 3d . 4d = 24
$$\therefore$$ d = 2
The sides are 6, 8, 10./p>
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