The base of an isosceles triangle measures 80 cm and its area is 2 `360 . cm^2` Find the perimeter of the triangle.

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#### Solution

Given:

Base = 80 cm

Area = 360

Area of an isosceles triangle=`(1/4 bsqrt(4a^2-b^2))`

⇒`360=1/4xx80sqrt(4a^a-80^2)`

⇒`360=20sqrt(4a^2-6400)`

⇒`18=2sqrt(a^2-1600)`

⇒`9=sqrt(a^2-1600)`

Squaring both the sides, we get:

⇒`81=a^2-1600`

⇒`a^2=1681`

⇒`a=41cm`

Perimeter=`(2a+b)`

=`[2(41+80)]=82+82=162cm`

So, the perimeter of the triangle is 162 cm.

Concept: Area of Circle

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