Question

side of a triangle are in the ratio 12: 17: 25 and its perimeter is 540cm. find its area.​

Answer 1

Answer:

Let the sides be 12x, 17x and 25x respectively.

Perimeter = 540 cm

⇒ 12x + 17x + 25x = 540

⇒ 54x = 540

⇒ x = 540/54

⇒ x = 10

a = 12 * 10 = 120 cm

b = 17 * 10 = 170 cm

c = 25 * 10 = 250 cm

Now,

$s = \frac{a + b + c}{2} \\ \\ s = \frac{540}{2} = 270$

Area =

$\sqrt{s(s - a)(s - b)(s - c)} \\ \\ \sqrt{270(270 - 120)(270 - 170)(270 - 250)} \\ \\ \sqrt{270 \times 150 \times 100 \times 20} \\ \\ \sqrt{81000000} \\ \\9000 \: cm {}^{2}$

Answer 2

Solution:-

Given:-

Ratio of the Sides of Triangle are 12 : 17 : 25.

Perimeter of Triangle = 540 cm.

To Find:-

Area of Triangle = ?

Find:-

Let the sides of the Triangle are 12x , 17x and 25x.

=) Perimeter of the Triangle = 12x + 17x + 25x

=) 540 = 54x

=) x = 540/54

=) x = 10.

Hence,

Sides of the Triangle are;

12x = 12 × 10 = 120 cm.

17x = 17 × 10 = 170 cm.

25x = 25 × 10 = 250 cm.

Now,

Semi- Perimeter of the Triangle = ( a+b+c)/2

=) s = 540/2 ( Given)

=) s = 270 cm.

Now,

Area of Triangle = √ { s (s-a)(s-b)(s-c)}

=) Area = √ { 270 ( 270 - 120)(270-170)(270-250)}

=) Area = √{ 270 × 150 × 100 × 20}

=) Area = √{ 81,000,000}

=) Area = 9000 cm².

Hence,

The Area of Triangle is 9000 cm².