The perimeter of a triangular garden is 300cm and its sides are in the

1.	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» 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 = $\dfrac{300}{15} = <klux>20</klux>$ The sides are:- ⇢ a = 3x = 3 × 20 = 60cm ⇢b = 5x = 5 × 20 = 100cm ⇢c = 7x = 7 × 20 = 140cm Semi - perimeter (s) = $\dfrac{300}{2} = 150$ $\rm Area\: of \: the \: triangle = \sqrt{s(s - a)(s - b)(s - c)}$ $\rm = \sqrt{150(150 - 60)(150 - 100)(150 - 140)}$ $\rm = \sqrt{150 \times 90 \times 50 \times 10}$ $\rm = \sqrt{6750000}$ $\rm = 1500\sqrt{3}$ $\underline{\boxed{\rm \therefore Area\: of\: triangle = 1500\sqrt{3} cm^{2}}}$