Question

Two sides of a parallelogram are 10 cm and 15 cm. If the altitude corresponding to the side of length 15 cm is 5 cm, then what is the altitude to the side of length 10 cm?

• A. 5 cm
• B. 7.5 cm
• C. 10 cm
• D. 15 cm

Answer 1

The correct option is B 7.5 cm

$\Rightarrow$ The given figure ABCD is a parallelogram with AO is the altitude corresponding to the side CD and CP is the altitude corresponding to side AD.

$\Rightarrow$ The given sides of the parallelogram are 10cm and 15cm.

So, take AD = 10cm, CD = 15cm and AO = 5cm.

We have to find length of CP.

$\Rightarrow$ Area of a parallelogram with with base AB and altitude AO is,

$\therefore$ Area of parallelogram $ABCD=AB\times AO$

$\Rightarrow 15\times 5$ -- (substituting values)

$\therefore$ Area of parallelogram $=75$ cm${}^2$

$\Rightarrow$ Area of parallelogram ABCD with base AD and altitude CP, as area will remain same.

$\therefore$ Area of parallelogram $ABCD=AD\times CD$

$\Rightarrow 75=10\times CD$

$\therefore CD=7.5$cm

We get 7.5 is the altitude to the side of length 10cm.