Question

ASO,
4. The sides of a triangle are in the ratio 5:12: 13, and its perimeter is
150 m. Find the area of the triangle.​

Answer 1

Step-by-step explanation:

let the side of triangle be:-

5x, 12x, 13x

perimeter of triangle = 5x+ 12x + 13x = 150 m

30x =150

x= 150 /30

x=5m

sides of triangle are 5x= 5×5 = 25 m

12x= 5× 12 = 60 m

13 x = 5× 13 = 65 m

Answer 2

Answer:

750 m square

Step-by-step explanation:

let the first side be 5x, second be 12x and third side be 13x

therefore, perimeter = 30

so, 5+12+13 = 30x

30x = 150

this implies x = 150 ÷ 30 = 5

therefore first side = 5×5 = 25m = a

second side = 5×12 = 60m = b

third side = 5×13 = 65m = c

area of ∆ by herons formula

2s = 150m

s = 150 ÷ 2 = 75

area = √s(s-a)(s-b)(s-c)

= √75(75-25)(75-60)(75-65)

=√75 × 50 × 15 × 10

= 5 × 5 × 3 × 5 × 5 × 2 × 5 × 3 × 5 × 2

= 5 × 5 × 5 × 3 × 2

= 750m square

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