Question

The perimeter of a triangle is 420m and its sides are in the ratio 6:7:8.Find the area of the triangle

Answer 1

Lets consider sides as 6x, 7x and 8x.
Perimeter = Sum of all sides
420 = 6x + 7x+ 8x
420 = 21x
x =
$\frac{420}{21}$
x = 20
sides of triangle = 6×20 , 7×20, 8×20
=120 cm,140 cm,160 cm
Area =
$\sqrt{s(s - a)(s - b)(s - c)}$
where s = semiperimeter = 420/2 = 210 cm
a b and c are respective sides.
$\sqrt{210(210 - 120)(210 - 140)(210 - 160)}$
=
$\sqrt{210 \times 90 \times 70 \times 50}$
=
$2100 \sqrt{5}$