A rectangular park has length of 60 m and breadth of 40 m. It has two crossroads of same width running in the middle of the park and rest of the park has been used as a lawn. The area of the lawn is 2109 sq m. What is the width of the road?
Answers
2. A rectangular park 60
m long and 40
m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. The area of the lawn is 2109sq. m. what is the width of the road?
Area of the park =60×40=2400m2
Given that area of the lawn =
2109 m2
∴ Total area of the cross roads=2400−2109=291 m2
Assume that the width of the cross roads =x
Then, total area of the cross roads
= Area of road
1
+ Area of road
2
- (Common area of the cross roads)
=
60
x
+
40
x
−
x
2
(Let's look in detail how we got the total area of the cross roads as
60
x
+
40
x
−
x
2
. As shown in the diagram, area of road
1
=
60
x
. This has the areas of the parts
1
,
2
and
3
given in the diagram. Area of road
2
=
40
x
. This has the parts
4
,
5
and
6
. You can see that there is an area which is intersecting (i.e. part
2
and part
5
) and the intersection area
=
x
2
.
Since
60
x
+
40
x
covers the intersecting area
(
x
2
)
two times (part
2
and part
5
), we need to subtract the intersecting area of
(
x
2
)
one time to get the total area. Hence total area of the cross roads
=
60
x
+
40
x
−
x
2
Now, we have
Total area of cross roads
=
60
x
+
40
x
−
x
2
But total area of the cross roads
=
291
m2
Hence,
60
x
+
40
x
−
x
2
=
291
⇒
100
x
−
x
2
=
291
⇒
x
2
−
100
x
+
291
=
0
⇒
(
x
−
97
)
(
x
−
3
)
=
0
⇒
x
=
3
(
x
cannot be
97
as the park is only
60
m long and
40
m wide)
Answer:
I think you..............
