Question

if the side of a triangle are in the ratio of 5:12:13: and it's perimeter is 450m find its area​

Answer 1

first take the sides as 5x , 12x and 13x

perimeter is given to us . So ,

5x + 12x + 13x = 450

30x = 450

x= 450 / 30

× = 15

Now ,

5x = 5 × 15 = 75

12x = 12 × 15 = 180

13x = 13 × 15 = 195

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Answer 2

Answer:

Perimeter of triangle = 450m (given)

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

On dividing 450m in the ratio 5:12:13, we get

∴ a = 5x m

∴ b = 12x m

∴ c = 13x m

we know that, perimeter of a triangle = Sum of all sides = a + b + c

∴ 450 = 5x + 12x + 13x

∴ 450 = 30x

∴ x = 15

Sides are:

∴ a = 5x = 75 m

∴ b = 12x = 180 m

∴ c = 13x = 195 m

Now,

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

Apply Heron's Formula of find the area of triangle.

Area = √S (S−a) (S−b) (S−c)

Where S= ( a + b + c ) ÷ 2

∴ S= (75 + 180 + 195) ÷ 2

∴ S = 450 ÷ 2

∴ S = 225 m

∴ Area = √[225 (225−75) (225−180 (225−195)]

= √(225 × 150 × 45 × 30)

= √45,562,500

= 6750 m^2

∴ Area of triangle is 6750 m^2

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