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The Base of an Isosceles Triangle Measures 80 Cm and Its Area is 2 `360 . Cm^2` Find the Perimeter of the Triangle. - Mathematics

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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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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 17 Perimeter and Areas of Plane Figures
Q 17

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