Question

The perimeter of a triangle field is 540 and its sides are in the ratio 25 is to 17 is to 12 find the area of the field also find the cost of plugging the field at rupees 5 per metre square

Answer 1

Step-by-step explanation:

Let the common multiplier of the given ratios be x.

Hence, the sides of the triangular field will be 25x, 17x and 12x.

Now, it is given that:

Perimeter of triangular field = 540 m

Therefore,

25x + 17x + 12x = 540

54x = 540

$x = \frac{540}{54} \\</p><p>\therefore x= 10 m\\</p><p>25x = 25\times 10= 250 \: m\\</p><p>17x = 17\times 10= 170 \: m\\</p><p>12x = 12\times 10= 120 \: m\\</p><p>$

Since, the numbers 250, 170 and 120 are Pythagorean triplets, means they form right triangles with 250 being the length of hypotenuse, hence

Area of triangle

$=\frac {1}{2} \times 170\times120\\</p><p>=170 /\times 60\\</p><p>=10200 \:m^2$

Cost of ploughing = 10200 x 5

= ₹51000