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Question

An unequal side of an isosceles triangle is 24 cm and its area is 60cm 2 find the perimeter of isosceles triangle .


Solution

Area of an isosceles triangle=1/2×base×height
Here, let the unequal side be the base ,
SoBase=24cm

Area of isosceles triangle= 1/2×24×height=60
So,12h= 60
Hence,h=60/12=5cm
Now height=5cm
base=24cm
So,hypotenuse=?
We know by Pythagoras theorem that (AB)²+(BC)²= (AC)²
Here
a=24/2=12cm (As base is divided into two parts by the altitude)
b=5cm
So,
(hypotenuse)²= (12)²+(5)²=169cm
So,side=hypotenuse=√169=13cm
So,
Perimeter=24cm+13cm+13cm=50cm

Hope this helps :)

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