Question

The perimeter of a triangular garden is 300cm and its sides are in the ratio 3:5:7 .Using Herons formula find the area of the triangular garden​

Answer 1

Step-by-step explanation:

The ratio of the sides of a triangle = 3 : 5 : 7

Let the common ratio of the sides be x

Therefore, the sides are 3x, 5x and 7x

As we know that:-

Perimeter of triangle = Sum of its sides

⇢3x + 5x + 7x = 300

⇢15x = 300

⇢x = $\dfrac{300}{15} = 20$

The sides are:-

⇢ a = 3x = 3 × 20 = 60cm

⇢b = 5x = 5 × 20 = 100cm

⇢c = 7x = 7 × 20 = 140cm

Semi - perimeter (s) = $\dfrac{300}{2} = 150$

$\rm Area\: of \: the \: triangle = \sqrt{s(s - a)(s - b)(s - c)}$

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

$\rm = \sqrt{150 \times 90 \times 50 \times 10}$

$\rm = \sqrt{6750000}$

$\rm = 1500\sqrt{3}$

$\underline{\boxed{\rm \therefore Area\: of\: triangle = 1500\sqrt{3} cm^{2}}}$