Question

The base of an isosceles triangle measures 24 cm and its area is 60 cm ² .Find its perimeter.

Answer 1

Altitude in an isosceles triangle is = h

$Area = \frac{1}{2}\ h\ a\ =\ 60\ cm^2 \\ \\ h\ =\ 2\ *\ \frac{60}{24} = 5 cm \\ \\ b^2 = \frac{a}{2}^2 + h^2 = 12^2 + 5^2 = 169 \\ \\ b = c = 13 cm \\ \\ Perimeter = a+b+c = 24+13+13 = 50 cm$

Answer 2

Area of an isosceles triangle=1/2×base×height
Here,Base=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