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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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