Question

The sides of a triangle are in the ratio 5:7:8and its perimiter is 300 find its area

Answer 1

Sides ratio = 5:7:8

Let x be side,

5x + 7x + 8x = 300

20x = 300

x = 300/20

x = 15

By substituting x = 15,

Side a = 5(15) =75

Side b = 7(15) = 105

Side c = 8(15) = 120

Area = $\sqrt{s(s-a)(s-b)(s-c)}$

s = a+b+c/2

s = 75+105+120

s = 300/2

s = 150

$\sqrt{150(150-75)(150-105)(150-120)}$

$\sqrt{150(75)(45)(30)}$

$\sqrt{3×5×5×2×5×5×3×3×3×5×3×5×2}$

$\sqrt{3×5×2×5×3×3×5}$

$\sqrt{6,750}$

$82.16$