Question

If the Perimeter of an isosceles triangle of base 12 cm is 30 cm then find its area

Answer 1

Answer:

40.24 sq cm

Step-by-step explanation:

perimeter of isosceles triangle 30cm

let the sides be a, b, c

a+b+c= 30

base side = 12

12 +b+c=30

b+c=18

in isosceles triangle two sides are equal

b=c

b+b=18. 2b = 18. b= 18/2 = 9

b=c=9

by herons formula

s=a+b+c/2 30/2= 15

area = ✓s(s-a)(s-b)(s-c)

$= \sqrt{15(15 - 12)(15 - 9)(15 - 9)} \\ = \sqrt{15 \times 3 \times 6 \times 6} \\ = \sqrt{5 \times 3 \times 3 \times 6 \times 6} \\ = 3 \times 6 \times \sqrt{5} \\ = 18 \times \sqrt{5} \\ = 40.24sq \: cm$