The perimeter of an isosceles triangle is 32 cm. If each equal side is $\frac{5}{6}$ of the base, find the area of the triangle.

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Step 1: Let each equal side of triangle be $x$ and base be $y$.
ATQ, $x + x + y = 32$
Also, $x = \frac{5}{6}y$
Step 2: $2x + y = 32 \Rightarrow 2 	imes \frac{5}{6}y + y = 32 \Rightarrow \frac{10y + 6y}{6} = 32$
Step 3: On solving these equations, we get $x = 10$ and $y = 12$.
$	herefore$ sides of the triangle are 10 cm, 10 cm, 12 cm.
Step 4: Semi-perimeter $= 16$ cm.
Area of the triangle $= \sqrt{16 	imes 6 	imes 6 	imes 4}$
Step 5: $= 48$ cm$^2$

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