Question

The base of an isosceles triangle measures 80 cm and its area is 360 $c{m}^2.$ Find the perimeter of the triangle.

Answer 1

Let, △ ABC be an isosceles triangle and let AL∥BC.

Given that BC= 80 cm and Area of △ABC=360cm^2

Therefore, 1/2×BC×AL=360cm^2

Therefore, 1/2×80×h=360cm^2

Therefore, 40×h=360cm^2

Therefore, h=36040=9cm

Now, BL=1/2BC

BL=1/2(80)=40 cm and AL=9cm

a = √BL^2+AL^2

a = √40^2+9^2

⇒a=√1600+81
⇒a=√1681=41cm

Perimeter = (41+41+80) = 162 cm

Perimeter of the triangle = 162 cm