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Question
The area of the isosceles triangle is `5/4 sqrt(11)` cm2, if the perimeter is 11 cm and the base is 5 cm.
Options
True
False
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Solution
This statement is True.
Explanation:
Suppose that side of isosceles triangle be a.
Now, perimeter of an isosceles triangle:
2s = 5 + a + a ...[2s = a + b + c]
11 = 5 + 2a
2a = 11 – 5
2a = 6
a = 3
Now, the formula of an area of isosceles triangle = `a/4 sqrt(4b^2 - a^2)`
So, area of an isosceles triangle = `(5sqrt(4 xx (3)^2 - (5)^2))/4`
= `(5sqrt(4 xx 9 - 25))/4`
= `5 xx sqrt(36 - 25)/4`
= `(5sqrt(11))/4` cm2
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