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Question

The longer side of a parallelogram is 54cm and the corresponding altitude is 16cm. If the altitude corresponding to the shorter side is 24cm, find the length of the shorter side.

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Solution

Let ABCD is a parallelogram with the longer side AB=54 cm and corresponding altitude AE=16 cm.
The shorter side is BC and the corresponding altitude is CF=24 cm.
We know that area of a parallelogram = base × height.
We have two altitudes and two corresponding bases.
By equating them we get,
12×BC×CF=12×AB×AE
On simplifying, we get
BC×CF=AB×AE
BC×24=54×16
BC=54×1624
BC=36 cm
Hence, the length of the shorter side BC=AD=36 cm.

1939807_1409203_ans_f5e7faccb29943c9a254a660fe747609.png

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