Question

Sides Of A Triangle Are In The Ratio 12 :17 : 25 and its perimeter is 540cm. Find its Area.

Answer 1

Answer:

9000cm^2 or 90 m^2

Step-by-step explanation:

given

sides are in the ratio 12 : 17 : 25

&

perimeter = 540

as we know that

perimeter of a triangle = (1st side + 2nd side + 3rd side)

=>

let

1st side be 12x

2nd............. 17x

3rd.............. 25x

now,

12x + 17x + 25x = 540

=> 54x = 540

=> x = 540/54

=> x = 10

so

1st side = 12x => 12×10 = 120cm

2nd side = 17x => 17×10 = 170cm

3rd side = 25x => 25×10 = 250cm

now

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

[ BY HERONS FORMULA]

where a, b, c are the three side and

s = semi perimeter => 1/2(a+b+c)

=> s = 1/2(120+170+250)

=> s = 1/2 × 540 = 270cm

now

area = √270(270-120) (270-170) (270-250)

=> area = √270(150×100×20)

=> area = √270 × 300000

=> area = √81000000

=> area = 9000 cm^2

or

area = 9000/100 = 90 m^2

Answer 2

$\huge\star{\green{\underline{\mathfrak{Answer: -}}}}$

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 = 540cm

12x + 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.