Find the possible dimensions of a rectangle whose area is 18sq.cm. (excluding decimal
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Answered by
0
Let
x
and
y
be the base and the height of the rectangle, respectively.
Since the area is 100
m
2
,
x
y
=
100
⇒
y
=
100
x
The perimeter
P
can be expressed as
P
=
2
(
x
+
y
)
=
2
(
x
+
100
x
)
So, we want to minimize
P
(
x
)
on
(
0
,
∞
)
.
By taking the derivative,
P
'
(
x
)
=
2
(
1
−
100
x
2
)
=
0
⇒
x
=
±
10
x
=
10
is the only critical value on
(
0
,
∞
)
y
=
100
10
=
10
By testing some sample values,
P
'
(
1
)
<
0
⇒
P
(
x
)
is decreasing on
(
0
,
10
]
.
P
'
(
11
)
>
0
⇒
P
(
x
)
is increasing on
[
10
,
∞
)
Therefore,
P
(
10
)
is the minimum
I hope that this was helpful.
Hence, the dimensions are
10
×
10
.
4
x
2
+
y
2
=
(
1
,
0
Answered by
0
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