Question

Construct a parallelogram $ABCD$ with $AB=24$ cm and $AD=16$ cm. The distance between AB and DC is $10$ cm. Find the distance between AD and BC.

• A. $25$ cm
• B. $15$ cm
• C. $13$ cm
• D. None of these

Answer 1

The correct option is B $15$ cm

The distance between AB and DC is the height (DE).
Area of the parallelogram ABCD = base x height = $24\times 10$ = $240$ sq cm
This is also the area of the same parallelogram with AD as the base and AH as the height.
height= $13$ width= $15$
Area of ABCD = ADx AH = $16\times AH$
But area = $240$sqcm
I.e. AH = $\frac{240}{16}=15$ cm