Question

Perimeter of a Triangle is 540 cm.
Sides are in the ratio 25;17:12 respectively.
Find lengths of sides?
Find the area of triangle
(start by taking x as the common multiple )
please solve this.

Answer 1

Hii friend,

ABC be a triangle.

Sides of triangle ABC are AB , BC and AC

Ratio of the sides of the triangle =25:17:12

Let X be common multiple to these side's.

Therefore,

Sides becomes 25X , 17X and 12X.

Perimeter of triangle = 540

25X+17X+12X = 540

54X = 540

X = 540/54

X= 10

Therefore,

25X =25 × 10 = 250cm

17X = 17 × 10 = 170cm

And,

12X = 12×10 =120cm

Therefore,

Length of each side of ∆ABC are 250 , 170 , 120 cm respectively.

Since,

All three sides of the triangle are different it means triangle ABC is isosceles.

Therefore,

Semi Perimeter(S) = 1/2 × (250+170+120)

=> 540/2 = 270 cm

S-A = 270-250 =20 cm

S-B = 270-170 = 100 cm

S-C = 270-120 = 150 cm

By using herons formula,

Area of triangle ABC = ✓S(S-A)(S-B)(S-C)

=> ✓270×20×100×150

=> ✓27000000

=> 5196.15 cm²

HOPE IT WILL HELP YOU.... :-)

Answer 2

here is your ans.....