Question

The sides of a triangle are in the racer 25 ratio 17 ratio 12 and its parameter is 540 metre find the area of the triangl

Answer 1

This is your answer

Answer 2

Let a, b and c be the sides of the triangle

a:b:c = 25:17:12

Let k be the common multiple on the RHS

a:b:c = 25k:17k:12k

So, a = 25k, b = 17k, c = 12k

Perimeter(∆) = 540

a + b + c = 540

25k + 17k + 12k = 540

54k = 540

k = 10

a = 25k = 25 x 10 = 250 units

b = 17k = 17 x 10 = 170 units

c = 12k = 12 x 10 = 120 units

For the triangle, semiperimeter(∆)

s = perimeter(∆)/2 = 540/2

s = 270 = 3² x 30

s - a = 270 - 250 = 20 = 4 x 5 = 2² x 5

s - b = 270 - 170 = 100 = 10²

s - c = 270 - 120 = 150 = 25x6 = 5² x 6

By heron's formula

ar(∆) = √[s(s-a)(s-b)(s-c)]

ar(∆) = √[(3² x 30)(2² x 5)(10²)(5² x 6)]

ar(∆) = 3 x 2 x 10 x 5√(30 x 6 x 5)

ar(∆) = 300 √(30 x 30) = 300 √ (30²)

ar(∆) = 300 x 30

ar(∆) = 9000 sq. units

Hence, area of the triangle is 9000 unit²