Question

The perimeter of a triangular field is 540m and it's sides are in the ratio 25:17:12 .find the area of the triangle .also find the cost of ploughing the field at rs 18.80 per 10m24

Answer 1

s= a+b+c
540 = 25x+17x+12x
540 =54x

$\frac{540}{54} = 10$

$25x = 25 \times 10 = 250 \\ 17x = 17 \times 10 = 170 \\ 12x = 12 \times 10 = 120$
$s = \frac{a + b + c}{2}$

$= \frac{250 + 170 + 120}{2}$
$\frac{540}{2} = 270$
$\sqrt{s(s - a)(s - b)(s - c)}$
$\sqrt{270(270 - 250)(270 - 170)(270 - 120)}$
$\sqrt{270 \times 20 \times 100 \times 150}$

$5 \times 2 \times 3 \times 3 \times 3 \times 2 \times 2 \\ \times 5 \times 5 \times 2 \times 2 \times \times 2 \\ \times 2 \times 5 \times 5 \times 5 \times 3 \times 2$
$3 \times 2 \times 5 \times 2 \times 5 \times 3 \times 2 \times 5$
$6 \times 10 \times 15 \times 10$
$600 \times 15$
9000cm2
the cost of ploughing the field at =rs 18.80
${10m}^{2} of \: the \: field \: of \: ploughing \: \\ the \: cost = 9000 \times \frac{18.80}{100} = \\ rs16920$