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