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An isosceles triangle has perimeter 3...

An isosceles triangle has perimeter `30 c m` and each of the equal sides os `12\ c mdot` Find the area of the triangle.

A

`8sqrt15cm^2`

B

`7sqrt15cm^2`

C

`9sqrt15cm^2`

D

`4sqrt15cm^2`

Text Solution

Verified by Experts

Here, Perimeter of the isosceles triangle `P = 30cm`
So, Semi-perimeter of the triangle, `s = 30/2 = 15cm`
Two sides of the triangle are `12cm`. So, `a=b = 12cm`
Third side, `c = P-a-b = 30-12-12 = 6cm`
Now, Area of the triangle, `A = sqrt(s(s-a)(s-b)(s-c))`(Herons formula)
`A = sqrt(15(3)(3)(9)) = 9sqrt15cm^2`
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Knowledge Check

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