Question

The perimeter of a triangular field is 540m and its sides are in the ratio 25: 17:12. Find the area of
the field. Also find the altitude corresponding to the longest side.
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Answer 1

★ Brainly Teacher ★

GIVEN : The perimeter of a triangular field = 540m

Let the sides are 25x , 17x , 12 x

Perimeter of a ∆ = sum of three sides

25x + 17x + 12x = 540

54x = 540

x = 10

1st side (a) - 25x = 25×10= 250m

2nd side(b)= 17x = 17×10= 170m

3rd side (c)= 12x = 12 × 10 =120m

Semi - perimeter ( S) = a+b+c/2

= (250 + 170+120)/2 = 540/2 = 270 m

Area of the ∆= √ S(S - a)(S - b)(S - c)

[By Heron’s Formula]

= √ S(S - 250)(S - 170)(S - 120)

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

= √ 270× 20×100×150

= √ 81000000

Area of the ∆= 9000 m²

Hence, the Area of the ∆= 9000 m²

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Step-by-step explanation:

Let the sides of the triangle be 25x, 17x and 12x

Given,

Perimeter of the triangle = 540 m

⇒ 540 = 25x + 17x + 12x

⇒ 540 = 54x

⇒ x = 540 / 54

⇒ x = 10

Thus, sides of the triangle are:

⇒ 25x = 25 × 10 = 250 m

⇒ 17x = 17 × 10 = 170 m

⇒ 12x = 12 × 10 = 120 m

Let, a = 250 m, b = 170 m and c = 120 m

Therefore, s = a + b + c / 2

⇒ s = 250 + 170 + 120 / 2

⇒ s = 540 / 2

⇒ s = 270

Therefore,

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

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

= √3 × 3 × 3 × 10 × 10 × 2 × 10 × 10 × 10 × 5 × 3

= 3 × 3 × 10 × 10 × 10

= 9000 m²