the length of a rectangle is increasing ata a ate of 8cm and is width is increasing at a rate of 3cm when the length is 20cm and
the width is 10cm how fast is the area of the rectangle
1 answer:
Answer:
us set up the following variables:
⎧
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎩
l
Length of Rectangle (cm)
w
Width of Rectangle (cm)
A
Area of Rectangle (
c
m
2
)
t
Time (s)
We are told that:
d
l
d
t
=
8
cm/s (const), and,
d
w
d
t
=
3
cm/s (const)
The Area of the rectangle is:
A
=
l
w
Differentiating wrt
t
(using the product rule) we get;
d
A
d
t
=
(
l
)
(
d
w
d
t
)
+
(
d
l
d
t
)
(
w
)
∴
d
A
d
t
=
3
l
+
8
w
So when
l
=
20
and
w
=
10
⇒
d
A
d
t
=
3
⋅
20
+
8
⋅
10
∴
d
A
d
t
=
60
+
80
∴
d
A
d
t
=
140
cm
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