The sides of a triangular park are in ratio 6:7:8 and perimeter is 420m Find it's area and te - Maths - Heron\s Formula

Question

The sides of a triangular park are in ratio 6:7:8 and perimeter
is 420m Find it's area and te length of the perpendicular drawn on
the biggest side

Varun.Rawat · Accepted Answer

Let the sides of the triangle are :

a = 6x , b = 7x , c = 8x

now, a + b + c = 420

so, 6x + 7x + 8x = 420 ⇒ x = 20

so, a = 120 cm , b = 140 cm , c = 160 cm

semi perimeter = s = 210 cm

$a r e a = \sqrt{s (s - a) (s - b) (s - c)} = \sqrt{210 \times 90 \times 70 \times 50} = \sqrt{66150000} = 2100 \sqrt{15} {c m}^{2}$

perpendicular = (2 × area) / longest side = 4200√15 / 160

= $\frac{105 \sqrt{15}}{4} c m$

The sides of a triangular park are in ratio 6:7:8 and perimeter is 420m. Find it's area and te length of the perpendicular drawn on the biggest side.