The altitude drawn to the base of an isosceles triangle is 8 cm and the perimeter is 32 cm. Find the area of the triagle?
Explanation:
In an isosceles triangle the altitde from vertical angle bisection the non equal side. ∴ BD = CD = a (say)
Also, AB + AC + BC = 32 ⇒ 2AB + 2a = 32 [AB = AC, isosceles triangle] ⇒ AB = AC = 16 - a
Now, △ADC is a right traingle. ⇒ (16 - a)2 = 82 + a2 ⇒ 256 + a2 - 32a = 64 + a2 ⇒ 192 = 32a ⇒ a = 6
Now, area of △ABC = 1/2 × AD × BC = 1/2 × 8 × 12 = 48 cm2.
Hence, option (d).
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