Question

Find the perimeter, of an isosceles triangle whose each equal side is 20 cm and it's area is 192 cm square. 9th class maths not only answer but also step by step explanation

Answer 1

Answer:

The equal sides of an isosceles triangle are 20 cm and its area = 192 sq cm.

Let the base angles be m.

The area of the triangle = [2*20 cos m * 20 sin m]/2 = 192, or

400 sin m cos m = 192, or

200 [2 sin m cos m] = 192, or

2 sin m cos m = 192/200 = 0.96, or

sin 2m = 0.96, or

2m = arc sin 0.96 = 73.73979529, or

m = 73.73979529/2 = 36.86989765 deg.

The base of the triangle = 2 * 20 cos 36.86989765 = 32 cm.

Hence the perimeter of the isosceles triangle = 20*2+32 = 72 cm.

Check: 2s = 72, or s = 36.

Area of isosceles triangle = [36{36–32)(36–20)(36–20]^0.5

= [36*4*16*16]^0.5 = 6*2*16 = 192 sq cm. Correct.