Question

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

Answer 1

Given:-

•Sides of a triangle are in the ratio 12:17:25

•Perimeter of the triangle=540cm

To find:-

•Area of the triangle

Solution:-

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

Perimeter of a triangle=Sum of 3 sides

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

=>54x=540

=>x=540/54

=>x=10

Thus,sides of the triangle are:'

•12×10=120cm(a)

•17×10=170cm(b)

•25×10=250(c)

Hence, a=120cm ,b=170cm and c=250cm.

Now,semiperimeter of the triangle(s)=1/2×540

=>270cm

•(s-a)=(270-120)=150cm

•(s-b)=(270-170)=100cm

•(s-c)=(270-250)=20cm

Now,according to Heron's formula,area of the triangle is :-

$= > \sqrt{s(s - a)(s - b)(s - c)}$

$= > \sqrt{270 \times 150 \times 100 \times 20}$

$= > \sqrt{81000000}$

$= > 9000 {cm}^{2}$

Thus,area of the triangle is 9000cm².

Answer 2

Step-by-step explanation:

Given:-

•Sides of a triangle are in the ratio 12:17:25

•Perimeter of the triangle=540cm

To find:-

•Area of the triangle

Solution:-

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

Perimeter of a triangle=Sum of 3 sides

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

=>54x=540

=>x=540/54

=>x=10

Thus,sides of the triangle are:'

•12×10=120cm(a)

•17×10=170cm(b)

25×10=250(c)

Hence, a=120cm ,b=170cm and c=250cm.

Now,semiperimeter of the triangle(s)=1/2×540

=>270cm

•(s-a)=(270-120)=150cm

•(s-b)=(270-170)=100cm

•(s-c)=(270-250)=20cm

Now,according to Heron's formula,area of the triangle is :-

= > \sqrt{s(s - a)(s - b)(s - c)}=>

s(s−a)(s−b)(s−c)

= > \sqrt{270 \times 150 \times 100 \times 20}=>

270×150×100×20

= > \sqrt{81000000}=>

81000000

= > 9000 {cm}^{2}=>9000cm

2

... hope it is helpful to you