Question

Perimater of a triangular field is 300cm and sides are in ratio 3:5:7 find it's area

Answer 1

Her the SOLUTION goes,

For triangular field,

Perimeter = 300 cm

Semiperimeter (s) = 300 / 2 = 150 cm

Now ,

Ratio of sides = 3: 5 : 7 = x (let)

1st side ( a ) = 3x

2nd side ( b ) = 5x

3rd side ( c ) = 7x

Perimeter = a + b + c = 3x + 5x + 7x = 15x

A.T.Q.

15x = 300

=> x = 300 / 15 = 20

Hence,

1st side ( a ) = 3x = 3× 20 = 60 cm

2nd side ( b ) = 5x = 5× 20 = 100 cm

3rd side ( c ) = 7x = 7 × 20 = 140

So,

$area = \sqrt{s(s - a)(s - b)(s - c)}$

$area = \sqrt{150(150 - 60)(150 - 100)(150 - 140)}$

$area = \sqrt{150(90)(50)(10)}$

$area = \sqrt{(3 \times 5 \times 10)(3 \times 3 \times 10)(5 \times 10)(10 )}$

$area = \sqrt{3 \times 3\times 5 \times 5 \times 10 \times 10 \times 3}$

$area = 3 \times 5\times 10\sqrt{3}$

$area = 150\sqrt{3} \: \: sq \: cm$

Hope you understood.

Enjoy Maths!!

(SK Study Point Siliguri)