Question

The altitudes to the sides AB and AD of parallelogram ABCD are 5 cm and 20 cm respectively. If the area of the parallelogram is 160 sq. cm, find its perimeter . ​

Answer 1

The altitudes to the sides AB and AD of parallelogram ABCD are 5 cm and 20 cm respectively. If the area of the parallelogram is 160 sq. cm, find its perimeter .

Refer to the attachment

Answer 2

Step-by-step explanation:

Perimeter=80 cm.

Step-by-step explanation:

Given:

Area of parallelogram ABCD=160 sq cm

As shown in the figure below, let DL=5cm, BM=20 cm

We know that area parallelogram ABCD=base\times heightbase×height

⇒160=AB\times5160=AB×5

⇒AB=\frac{160}{5}AB=

5

160

⇒AB=32 cm

Also area of parallelogram ABCD=BM\times ADBM×AD

⇒160=$20\times AD$

⇒AD=8 cm.

We know that perimeter of parallelogram ABCD=2(AB+AD)

=2(32+8)

=80 cm