In an isosceles right-angled triangle, the perimeter is 30 m. Find its area (in m2). (Rounded off to the nearest integral value)
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Correct answer: C
Explanation
The correct answer is option 3 i.e. 39.
Let the length of each leg = a
Hypotenuse = √(a2 + a2) = a√2
So, a + a + a√2 = 30
⇒ 2a + a√2 = 30
⇒ a(2 + √2) = 30
⇒ a = 30/(2 + √2) = 15(2 - √2)
Area = (1/2)a2 = (1/2) × [15(2 - √2)]2
= (1/2) × 225(4 + 2 - 4√2)
= (1/2) × 225(6 - 4√2)
= 112.5(6 - 5.6568) [√2 = 1.4142]
= 38.626
≈ 39 m2
Hence, the area of the isosceles right-angled triangle is 39 m2.