Question

The perimeter of parallelogram ABCD is 96cm. AD is 9 cm more than twice AB. Find the lengths of all four sides of ABCD.

Answer 1

Answer: AB=11

AD=31

BC=31

CD=11

Explanation:

Answer 2

Answer:
`AB=CD=13\ cm\ \text{and}\ BC=AD=35\ cm`

Explanation:

Given

ABCD is a parallelogram

Side AD is 9 cm more than twice AB i.e.

`AD=9+2AB`

Also, for parallelogram

`\Rightarrow AB=CD,BC=CD`

Perimeter is the sum of the sides

`\therefore AB+BC+CD+AD=96\\\Rightarrow AB+AD+AB+AD=96\\\Rightarrow AB+AD=48\\\\\text{Substitute the value of AD}\\\Rightarrow AB+9+2AB=48\\\Rightarrow 3AB=39\\\Rightarrow AB=13`

So,
`AD=35\ cm`

Thus,
`AB=CD=13\ cm\ \text{and}\ BC=AD=35\ cm`