Question

find the area of a triangle whose perimeter is 168m and two of its sides are 56m and 60​

Answer 1

Answer:

Sides of triangle are 56 m, 60 m, x m

Perimeter of triangle = Sum of all sides = 56+60+x = 168m

x = 168-60-56 m

x = 52 m

Area of triangle with 3 sides given(Heron's formula) = $\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$

$s=\frac{a+b+c}{2}=\frac{168}{2}=84$

Area = $\sqrt{84\left(84-60\right)\left(84-56\right)\left(84-52\right)}$

        = $\sqrt{84\times24\times\:28\times \:32}$

        = $\sqrt{(2 \times 2 \times3 \times 7)(2 \times 2 \times 2 \times 3)(2 \times 2 \times 7)(2 \times 2 \times 2 \times 2 \times 2)}$

        = $2 \times 32 \times 3 \times 7$

        = $1344 \: m^2$