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Question
Find the area of an isosceles triangle whose perimeter is 72cm and the base is 20cm.
Solution
The sum of the equal sides of the given Isosceles triangle
= 72 - 20
= 52
So, each the equal sides of the given Isosceles triangle =
`(1)/(2)(52)`
= 26cm
We know that, Area of a Triangle whose sides are a, b, and c and semiperimeter is s is given by `sqrt("s"("s" - "a")("s" - "b")("s" - "c")); "s" = ("a" + "b" + "c")/(2)`
Here, sides are 26cm, 26cm and 20cm
s = `"P"/(2)`
= `(72)/(2)`
= 36
Area
= `sqrt(36(36 - 26)(36 - 26)(36 - 20)`
= `sqrt(36(10)(10)(16)`
= 6 x 10 x 4
= 240cm2.
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