Question

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

Answer 1

Answer:

Step-by-step explanation:

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

Let the common ratio be x then sides are 12x, 17x and 25x

Perimeter of the triangle = 540cm12x + 17x + 25x = 540 cm⇒ 54x = 540cm⇒ x = 10

Sides of triangle are,

12x = 12 × 10 = 120cm

17x = 17 × 10 = 170cm

25x = 25 × 10 = 250cm

Semi perimeter of triangle(s) = 540/2 = 270cm

Using heron's formula,

Area of the triangle = √s (s-a) (s-b) (s-c)

                                 = √270(270 - 120) (270 - 170) (270 - 250)cm²                                                      = √270 × 150 × 100 × 20 cm² = 9000 cm²

Answer 2

Answer:

let side = x

Step-by-step explanation:

12x + 17x + 25 = 540

54x = 540

x = 540 / 54

x = 10

lets substitute the value of x in the ratio's we get,

12(10)  ,   17(10)   ,   25(10)

therefore the sides are 120 , 170 , 250

lets use heron's formula to find area,

semiperimeter = 540/2

270cm

√s(s-a)(s-b)(s-c)

√270(270-120)(270-170)(270-250)

√270(150)(100)(20)

√81000000

9000 $cm^{2}$

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