Arithmetic Ability
Area

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Q.

The altitude drawn to the base of an isosceles triangle is 8 cm and the perimeter is 32 cm. Find the area of the triangle.

View Answer

Correct choice: B

Explanation:

Let ABC be the isosceles triangle and AD be the altitude Let AB = AC = x. Then, BC = (32 - 2x). Since, in an isosceles triangle, the altitude bisects the base, so BD = DC = (16 - x). In triangle ADC,(AC)2=(AD)2+(DC)2 ⇒x2=(8)2+(16−x)2⇒x=10 BC = (32- 2x) = (32 - 20) cm = 12 cm. Hence, required area = 12*BC*AD=12*12*8=48cm2
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