Question

The sides of triangle are in the ratio 12:17:25 and its perimeter is 540 cm. Find its area

Answer 1

Answer:

Let the no.be x

A to q

12x+17x+25x=540

=54x=540

=x=10

now sides =120

170 and 250

Answer 2

$\huge\mathfrak{Answer}$

Given that the sides of triangle are in the ratio of 12:17:25.

Let sides of triangle in cm are 12x, 17x, and 25x.

Perimeter of triangle = 540 cm (given)

=> 12x + 17x + 25x = 540cm

=> 54x = 540 cm

$= > x = \frac{540}{54} cm$

=> x = 10cm

Now sides of triangle are

12x = 12×10=120 cm

17x = 17×10=170 cm

and 25x = 25×10= 250 cm

$Semiperimeter, of triangle \: = \frac{perimeter }{2}$

$= \frac{540}{2} cm \: = 270cm$

Using Hero's Formula;

Area of triangle

$= \sqrt{270(270 - 120)(270 - 170)(270 - 250)} {cm}^{2}$

$= \sqrt{270 \times 150 \times 100 \times 20} {cm}^{2}$

$= \sqrt{30 \times 3 \times 3 \times 30 \times 5 \times 10 \times 10 \times 2 \times 2 \times 5} {cm}^{2}$

$\sqrt{2 \times 2 \times 3 \times 3 \times 5 \times 5 \times 10 \times 10 \times 30 \times 30} {cm}^{2}$

= 2 × 3 × 5 × 10 × 30 cm²

= 9000 cm²

Hence, area of required triangle is 9000 cm².