Question

sides of triangle are in ratio 3:5:7 and its perimeter is 300 m.find its area

Answer 1

Ratio = 3 : 5 : 7 (Given)

Define x:

Let x be the constant ratio

Ratio = 3x : 5x : 7x

Solve x:

Perimeter = 300 m (Given)

3x + 5x + 7x = 300

15x = 300

x = 300 ÷ 15 = 20

Find the sides:

3x = 3(20) = 60 m

5x = 5(20) = 100 m

7x = 7(20) = 140 m

Find the semi-perimeter:

Perimeter = 300 m

Semi-perimeter = 300 ÷ 2 = 150m

Find the area:

Area = √p(p-a)(p-b)(p-c)

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

Area = √6750000

Area = 1500√3 m²

Answer: The area is 1500√3 m²

Answer 2

Given:

Sides of triangle in ratio=3:5:7 Perimeter of the same triangle =300m

Solution: Perimeter =side 1 +2+3

Let x is common in ratio

3x+5x+7x=300------(1)

Add the given terms

15x=300

x=20

Substitute x=20 in (1)

3*20+5*20+7*20=300

60+100+140=300

300=300

Therefore LHS=RHS

Therefore our answer is correct