Question

The area of an isosceles triangle ABC is 48 cm${}^2$, where AB = AC. If the perimeter of the triangle and its altitude AD on BC are 32 cm and 8 cm respectively, then the length of the equal sides is equal to

• A. 8 cm
• B. 10 cm
• C. 12 cm
• D. 13 cm

Answer 1

The correct option is B 10 cm


Area of $\Delta ABC=\frac{1}{2}\times \text{Base}\times \text{Altitude}$
$\Rightarrow 48=\frac{1}{2}\times BC\times AD$
$\Rightarrow 48\times 2=BC\times 8$ ($\because AD=8cm$)
$\Rightarrow BC=12cm$ …..(i)
Perimeter of $\Delta ABC=32cm$
$\Rightarrow AB+BC+AC=32$
$\Rightarrow 2AB+12=32$ ($\because AB=AC$ and $BC=12cm$)
$\Rightarrow AB=\frac{32-12}{2}=10cm$
Thus, the length of the equal sides of $\Delta ABC$ is 10 cm.
Hence, the correct answer is option (b).