Question

A rectangular pool has length of 6 m and 3 m width. The pool is surrounded by a uniform edge with width x m. Given the area of the pool side is 32 m². Form a quadratic function and equation for the situation.​

Answer 1

you can solve this problem with the help of this example :

A rectangular pool 20 meters wide and 60 meters long is surrounded by a walkway of uniform width. If the total area of the walkway is 516 square meters, how wide, in meters, is the walkway?

Sol:

A rectangular pool has length l=60m & breadth b=20m.

It has a surrounding walkway of area =516m

2

.

Area (pool) =60×20=1200m

2

Let us take the width of the walkway =

2

X

.

∴ The length as well as the breadth of the area (pool+walkway) will be increased by X

So the length =l of the area (pool+walkway) =(60+X)m and the breadth =b=(20+X)m

∴ Area (pool+walkway) =l×b=[(60+X)×(20+X)]m

2

.

∴ Area (walkway) = Area (pool+walkway) - Area (pool)

=(60+X)×(20+X)−1200=516m

2

....(given)

⇒X

2

+80X−516=0

⇒X=−86 or X=6.

We reject the negative value as X is a length.

So X=6m.

Ans- The width of the walkway =

2

X

=3m.