Question

sides of a triangle are in the ratio 12:17:25 and it's perimeter is 540cm find it's area
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Answer 1

Given :

⬤ Sides of triangle are in the ratio 12:17:25 .

⬤ Perimeter of triangle = 540 cm.

To Find :

⬤ Area of triangle .

Solution :

Let :

• The sides of a triangle be 12x , 17x and 25x.
• a = 12x , b = 17x , c = 25x

$\sf{12x+17x+25x=540}$

54x = 540

x = 540/54

x = 10 cm

Therefore , The Value of x is 10 cm .

Hence ,

Angle 1 = 12x

= 12(10)

= 120 cm.

Angle 2 = 17x

= 17(10 )

= 170 cm.

Angle 3 = 25x

= 25(10 )

= 250 cm.

Now :

s = a+b+c/2

s = 120 + 170 + 250/2

s = 540/2

270

So ,

$\sf{Area=\sqrt{s(s-a)\:(s-b)\:(s-c)}}$

√270 (270 - 120) (270-170) (270-250)

√270 (150) (100) (20)

√3 × 3 × 5 × 2 × 5 × 2 × 5 × 2

9000 cm²

Therefore , The Area of the triangle is 9000 cm².