Question

The base of isoscless triangle is 24 and area 192 find perimeter

Answer 1

GIVEN: ABC an isosceles triangle, AB=AC. So angle B = angle C. Base BC = 24cm,

TO FIND: The perimeter(AB + BC + AC) =?

CONSTRUCTION: AM perpendicular to BC.

Since triangle AMB is congruent to triangle AMC( by RHS congruence criterion)

So, M is the mid point of BC. So, BM = 12cm

Since area(triangle ABC) = 1/2 * BC * AM

=> ar(tri ABC) = 1/2 * 24 * AM = 192

=> AM = 192/ 12 = 16cm.

Now in right triangle AMB

AB² = AM² + BM²

=> AB² = 16² + 12²

=> AB² = 256 + 144 = 400

=> AB = √400 = 20cm

So, AC = 20cm

So,perimeter=20+20+24 =64cm

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