Question

The longer side of a parallelogram is 81 cm and the corresponding altitude is 16 cm. If the length of the shorter side is 24 cm, what is the altitude corresponding to the shorter side?

• A. 36 cm
• B. 48 cm
• C. 54 cm
• D. 24 cm

Answer 1

The correct option is C

54 cm

Given, longer side of the parallelogram = 81 cm
altitude corresponding to the longer side = 16 cm
shorter side of the parallelogram = 24 cm
Let, the altitude corresponding to the shorter side be $x$.
Now, Area of the parallelogram = Longer side $\times$ altitude corresponding to longer side = Shorter side $\times$ altitude corresponding to shorter side
$\Rightarrow 81cm\times 16cm=24cm\times x$
$\Rightarrow$ $x=\frac{81\times 16}{24}$ cm
$\Rightarrow x=54cm$
$\therefore$ The altitude corresponding to the shorter side is 54 cm long.