Question

The sides of triangle are 7:5:3 and perimeter is 300m. Find its area?

Answer 1

Let the sides be 7a, 5a and 3a

Perimeter = 7a + 5a +3a

=> 300 = 15a

=> a = 20

First side = 140 m

Second side = 100 m

Third side = 60 m

Semi Perimeter = 300 / 2

s = 150 m

(s-a) = (150 - 140) = 10

(s-b) = (150 - 100) = 50

(s-c) = (150 - 60) = 90

Area = sqrt ( 150 × 10 × 50 × 90)

= 100 sqrt ( 15 × 5 × 9)

= 100 × 5 × 3 sqrt (3)

= 1500 root 3 m^2

Answer 2

Let the common ratio be x.

Then the sides of the triangle be 7x,5x,3x.

Given that perimeter of a triangle is 300m.

= > 7x + 5x + 3x = 300

= > 15x = 300

= > x = 300/15

= > x = 20.

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Now,

1st side = 7x

= 140m.

2nd side = 5x

= 100m.

3rd side = 3x

= 60m.

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We know that semiperimeter of a triangle = perimeter/2

= > s = 300/2

= > s = 150m.

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We know that Area of triangle s = $\sqrt{s(s - a)(s - b)(s - c)}$

$= > \sqrt{150(150 - 140)(150 - 60)(150 - 100) }$

$= > \sqrt{150(10)(90)(50)}$

$= > \sqrt{150 * 45000}$

$= > \sqrt{6750000}$

$= > 1500\sqrt{3}$

Therefore, the area of triangle is : $1500\sqrt{3}$

Hope this helps!