Question

The base of an isosceles triangle measure 24 cm and its area is 192cm^2
. Find its perimeter. ​

Answer 1

Answer:

64cm

Step-by-step explanation:

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