Question

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

Answer 1

Answer:

36

Step-by-step explanation:

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,

2

1

×BC×CF=

2

1

×AB×AE

On simplifying, we get

BC×CF=AB×AE

⇒BC×24=54×16

⇒BC=

24

54×16

⇒BC=36 cm

Hence, the length of the shorter side BC=AD=36 cm.