Question

Sides of a triangle are in the ratio 12 : 17 : 25 and its perimeter is 54 cm. Find its area.​

Answer 1

Answer:

A = 9000 cm²

Step-by-step explanation:

Let x be common ratio

∴ Sides of triangle will be: 12x,17x and 25x

⇒Perimeter =540 cm(given)

⇒12x+17x+25x=540 cm

⇒54x=540 cm

⇒x=10cm

Sides of triangle:

a = 12 × 10 = 120 cm

b =17 × 10 = 170 cm

c = 25 × 10 = 250 cm

⇒S = $\frac{540}{2}$ = 270 cm

A = s(s−a)(s−b)(s−c)

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

=$\sqrt{270 * 150 * 100 * 20 }$

= $\sqrt{81000000}$

A = 9000 cm²

HOPE IT HELPS!!

Answer 2

Answer:

90 cm²

Step-by-step explanation:

given the ratio of the sides of the triangle 12:17:25

let x be the proportionality constant,

=> the sides are 12x,17x,25x

so, perimeter will be 12x+17x+25x = 54x

given 54x = 54cm

=> x = 1

so, the sides are 12cm, 17cm, and 25cm

=> we here have a scalene triangle

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we know area of the scalene triangle with sides a,b&c is,

A = $\sqrt{s(s-a)(s-b)(s-c)}$   where s = $\frac{(a+b+c)}{2}$  

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here, s = (12+17+25)/2 = 54/2 = 27

so, Area = $\sqrt{27 (27-12)(27-17)(27-25)}$ cm²

             = $\sqrt{27 (15)(10)(2)}$ cm²

             = $\sqrt{3*3*3*3*5*5*2*2}$ cm²

             = $\sqrt{3^2*3^2*5^2*2^2}$ cm²

             = $3*3*5 *2$ cm²

             = 90 cm²