Question

The area of an isosceles triangle is 48 cm². If the length of the altitude to the non-equal side is 8cm, then the length of the equal sides of the triangle is​

Answer 1

Answer:

The base can either be of 12cm or of 16cm , both are correct.

Step-by-step explanation:

The area of a triangle is given by [ab sin C]/2. In this case,

area = 48 = [10*10 sin C]/2, or

sin C = 48*2/100 = 0.96.

Or <C = arc sin 0.96 = 73.73979529 deg

<C/2 = 73.73979529 /2 = 36.86989765 deg

Half the base = 10 sin 36.86989765 = 6 cm

Hence the base is 12 cm.

Check: Semi-perimeter = [10+10+12]/2 = 16

Applying Heron’s formula, Area of triangle = [16(16–10)(16–10)(16–12)]^0.5

= [16*6*6*4]^0.5 = 8*6 = 48 sq cm. Correct.

Hence the base is 12 cm.