Question

find the area of triangle whose two sides are 18cm and 10cm and perimeter is 42cm ans2 (square root )11cm2

Answer 1

a=18

b=10

perimeter=42

perimeter of triangle= a + b + c

42 = 18 + 10 + c

c=42-28

c= 14



semiperemeter or s= perimeter/2


s=42/2=21


s-a= 21 - 18 = 3

s-b= 21 -10= 11

s-c= 21-14 =7



according to heron formulae

area of triangle

$= \sqrt{s(s - a)(s - b)(s - c)} \\ \\ = \sqrt{21 \times 3 \times 11 \times 7} \\ \\ = \sqrt{3 \times 7 \times 3 \times 11 \times 7} \\ \\ = \sqrt{3 \times 3 \times 7 \times 7 \times 11} \\ \\ \sqrt{ {3}^{2} \times {7}^{2} \times 11 } \\ \\ 3 \times 7 \times \sqrt{11 } \\ \\ 21 \sqrt{11}$