Question

the parimeter ofa tringle is 300 and it's sides are in the ratio 3:5:7find the area of the triangle​

Answer 1

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

$\sf{\huge{\underline{\green{Given :-}}}}$

• The perimeter of a triangle is 300 cm².

• The sides are in the ratio 3:5:7 .

$\sf{\huge{\underline{\green{To\:Find :-}}}}$

• The area of the triangle .

$\sf{\huge{\underline{\green{Answer :-}}}}$

Let the sides of triangle are 3x, 5x & 7x .

We have,

The perimeter of a triangle is 300 cm². -----(1)

We know that the perimeter of triangle = s + s + s

➝ 3x + 5x + 7x ----(2)

Equating , 1 & 2

➝ 3x + 5x + 7x = 300

➝ 15x = 300

➝ x = 300/15

➝ x = 20

3x = 3 × 20 = 60

5x = 5 × 20 = 100

7x = 7 × 20 = 140

We have all sides unequal in the following triangle.

Hence, the triangle is scalene .

We know that ,the area of scalene triangle is √s(s - a)(s - b) (s - c) .

➝ √s(s - a)(s - b) (s - c)

s = 300 ÷ 2 = 150

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

➝ Area = √150(90) ( 50)(10)

➝ Area = √150(90) ( 50)(10)

➝ Area = √150 × 45000

➝ Area = √6750000

➝ Area = 1500√3 m²

Hence, The area of the triangle is 1500√3 m² .