Question

perimeter of a triangle is 300m .if its sides are in the ratio of 3:5:7. find area of triangle.​

Answer 1

Answer:

Define x:

Ratio = 3 : 5 : 7

Let x be the constant ratio

Ratio = 3x : 5x : 7x

Find the lengths:

3x + 5x + 7x = 15x

15x = 300

x = 20

3x = 3(20) = 60 m

5x = 5(20) = 100 m

7x = 7(20) = 140 m

Find the area;

Area = √p(p - a)(p - b) (p - c)

p = 300 ÷ 2 = 150

Area = √150(150 - 60) ( 150 - 100)(150 - 140)

Area = √6750000

Area = 1500√3 m²

Answer: The area of the triangle is 1500√3 m²

Answer 2

Answer:

2598.07 m²

Step-by-step explanation:

Given that the sides are in the ratio of 3:5:7. Therefore, the sides would be 3x, 5x and 7x

3x + 5x + 7x = 300

15x = 300

x = 20

So, the sides are 60m, 100m, 140m.

By Heron's Formula,

s = (60 + 100 + 140)/2 = 300/2 = 150

s - a = 150 - 60 = 90

s - b = 150 - 100 = 50

s - c = 150 - 140 = 10

Area of triangle = √[s(s-a)(s-b)(s-c)]

= √150*90*50*10

= √6750000

= 2598.07 m²

Hope it Helps ^_^