The perimeter of a triangle is 288 m and the ratioof the sides is 3: 4

1.	The perimeter of a triangle is 288 m and the ratioof the sides is 3: 4:5. Find the area of the triangle.
Answer» Question: The perimeter of a TRIANGLE is 288 m and the RATIO of the sides is 3: 4:5. Find the area of the triangle. Given: The perimeter of a triangle is 288 m Ratio of sides = 3:4:5 To find: Area of the triangle FORMULA Used: Perimeter = 3s Area = $\sqrt{s(s-a)(s-b)(s-c)}$ Solution: LET the sides be side 1 = 3x side 1 = 4x side 1 = 5x Perimeter = 3s $288 = 3x + 4x + 5x\\\\288 = 12x \\\\x= 288/12\\\\x = 24$ 3x = 3 x 24 = 72 4x = 4 x 24 = 96 5x = 5 x 24 = 120 a = 72 m b = 96 m c = 120 m Through herons formula we can find the area when 3 sides are given $\sqrt{s(s-a)(s-b)(s-c)}$ where , a = 72 b = 96 c = 120 $s =\frac{a+b+c}{2}$ s= $\frac{288}{2}$ $s=144cm$ $\sqrt{144(144-72)(144-96)(144-120)}$ $\sqrt{144(72)(48)(24)}$ $\sqrt{11943936\:\: m}$ $= <klux>3456</klux> \:m^2$ Area = 3456 m² Answer: Area of the triangle whose perimeter is 288 cm is 3456 m²