Answer:
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.
