Find the area of an isosceles triangle having each of whose equal sides is 13 cm and whose base is 24 cm.

Options

A. 60 `cm^(2)`
B. 70 `cm^(2)`
C. 80 `cm^(2)`
D. 90 `cm^(2)`

Answer

A

Explanation

Here, a = 13 cm, b = 13 cm and c = 24 cm.
`therefore" "s=(1)/(2)(a+b+c)=(1)/(2)(13+13+24)cm = 25 cm`.
`therefore" "(s-a)=(25-13)cm=12cm, (s-b)=(25-13)cm = 12 cm and (s-c)=(25-24)cm = 1cm`.
So, by Heron's formula,
`Delta = sqrt(s(s-a)(s-b)(s-c))`
`= sqrt(25 xx 12 xx 12 xx 1)cm^(2)=(5xx12)cm^(2)=60cm^(2)`.
Hence, the area of the given triangle is 60 `cm^(2)`.