Let the length of the sides of triangle be 2x, 3x and 4x. Perimeter of triangle = 180cm ⇒ \(2x +3x + 4x = 180\) ⇒ \(9x = 180\) ⇒ \(x = \frac{180}{9}\) = 20cm Then the sides of the triangle are: \(2x = 2\times20 = 40cm; 3x = 3\times20\) = 60cm and \(4x\) = 4\(\times20 \)= 80cm Using Heron's formula Area of triangle = \(\sqrt s(s-a)(s-b)(s-c)\) Where s = \(\frac{a + b + c}{2}\) Let a = 40cm, b = 60cm, c = 80cm and s = \(\frac{40 + 60 + 80}{2} = \frac{180}{2}\) = 90cm ⇒ A = \(\sqrt90 (90 - 40) (90 - 60) (90 - 80) = \sqrt90 \times 50 \times 30 \times 10 = \sqrt1350000\) ∴ A =1162cm\(^2\) (to the nearest cm\(^2)\)