Question

the base of an isosceles triangle measures 80cm and its area is 360 cm 2 .Find the perimeter of the triangle. In herons formula?​

Answer 1

Answer:

Let us assume the equal sides to be x.

Given that base=80 cm.

=> Height of the isosceles triangle=\sqrt{x^{2}-40^{2}}

x

2

−40

2

(using pythagoras theorem)

So, area=\frac{1}{2}bh

2

1

bh

360=\frac{1}{2}*80*\sqrt{x^{2}-40^{2}}

2

1

∗80∗

x

2

−40

2

9=\sqrt{x^{2}-40^{2}}

x

2

−40

2

81={x^{2}-40^{2}}x

2

−40

2

x^{2}=1681

x=41cm

=> Perimeter=41+41+80=162cm.