Question

7. The perimeter of a triangular field is 540 m and its sides are in the ratio
25:17:12. Find the area of the field. Also, find the cost of ploughing the
field at 5 per m²

Answer 1

Answer:

•GIVEN:- perimeter = 540m

and sides are in ratio 25:17:12

So, the sides are 25x , 17x , 12x where x is any positive no.

then ,25x + 17x + 12x = 540

54x = 540

x = 10

25x = 25 * 10 = 250

17x = 17*10 = 170

12x = 12*10 = 120

So, the sides are 250m , 170m & 120m.

now, the semi - perimeter is S = 540/2 = 270 m

we know the Heron's formula:-

area of triangle = \sf{\sqrt{s(s - a)(s - b)(s - c)}}

s(s−a)(s−b)(s−c)

where, a,b,c is the sides of triangle and s is the semi-perimeter.

now, the area of the triangle is

= \sf{\sqrt{S(S - 250)(S - 170)(S - 120)}}

S(S−250)(S−170)(S−120)

m²

= \sf{\sqrt{270*(270 - 250)*(270 - 170)*(270 - 120)}}

270∗(270−250)∗(270−170)∗(270−120)

m²

= \sf{\sqrt{270*20*100*150}}

270∗20∗100∗150

m²

= \sf{\sqrt{81000000}}

81000000

m²

= 9000m²

Hence, the area of triangle = 9000m²

•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

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