The base of an isosceles triangle measures 80 cm and its area is 360 c

1.	The base of an isosceles triangle measures 80 cm and its area is 360 cm2. Find the perimeter of the triangle.
Answer» Let two sides of an isosceles triangle are of same measure “a”. Base = b = 80 cm Area of triangle = 360 cm². (given) We know, Area of isosceles triangle = 1/4 × b√(4a² – b²) 360 = 1/4 x 80 x √(4a² – (80)²) 360 = 20 x √(4a² – 6400) 360 = 20 x 2√(a² – 1600) 9 = √(a² – 1600) Squaring both sides 81 = a² – 1600 a = 41 => a = 41 cm Perimeter of triangle = Sum of all the sides = 41 + 41 + 80 = 162 Perimeter of triangle is 162 cm.

The base of an isosceles triangle measures 80 cm and its area is 360 cm2. Find the perimeter of the triangle.

Answer»

Let two sides of an isosceles triangle are of same measure “a”.

Base = b = 80 cm

Area of triangle = 360 cm². (given)

We know, Area of isosceles triangle = 1/4 × b√(4a² – b²)

360 = 1/4 x 80 x √(4a² – (80)²)

360 = 20 x √(4a² – 6400)

360 = 20 x 2√(a² – 1600)

9 = √(a² – 1600)

Squaring both sides

81 = a² – 1600

a = 41

=> a = 41 cm

Perimeter of triangle = Sum of all the sides = 41 + 41 + 80 = 162

Perimeter of triangle is 162 cm.