Question

The base of an isosceles triangle having the base 16 cm. If its perimeter is 36 cm, find the
area​

Answer 1

Step-by-step explanation:

perimeter of isosceles triangle = 36 cm

base = 16 cm

equal sides be x cm

x + x + 16 = 36

2x = 36 - 16

2x = 20

x = 20/2 = 10

therefore the sides of isosceles triangle are 10cm, 10cm & 16 cm

we use herons formula to find the area of triangle with sides given

area = √s(s-a)(s-b)(s-c)

s = (a+b+c)/2

a, b, c are the sides of triangle

$s = \frac{10 + 10 + 16}{2} \\ = \frac{36}{2} = 18 \\ \\ area = \sqrt{18(18 - 10)(18 - 10)(18 - 16)} \\ = \sqrt{18 \times 8 \times 8 \times 2} \\ = \sqrt{3 \times 3 \times 2 \times 8 \times 8 \times 2} \\ = 3 \times 2 \times 8 \\ = 48 \: {cm}^{2}$

area of the isosceles triangle = 48 sq cm

hope you get your answer