The perimeter of an isosceles triangle is 40 cm. The base is two third of the sum of equal sides. Find the length of each side.

Let the length of equal sides be x cm.

Length of base = $\dfrac{2}{3}(x + x) = \dfrac{2}{3} \times 2x = \dfrac{4x}{3}$ cm.

Given,

Perimeter = 40 cm

$\therefore x + x + \dfrac{4x}{3} = 40 \\[1em] \Rightarrow 2x + \dfrac{4x}{3} = 40 \\[1em] \Rightarrow \dfrac{6x + 4x}{3} = 40 \\[1em] \Rightarrow 10x = 120 \\[1em] \Rightarrow x = 12 \text{ cm}.$

Length of Base = $\dfrac{4x}{3}$ = $\dfrac{4}{3} \times 12$ = 16 cm

Hence, length of equal sides = 12 cm and length of base = 16 cm.