Question

A rectangle's base remains 0.5 cm while its height changes at a rate of 1.5 cm/min.

Answer 1

The area of the rectangle is changing at

0.75 sq.cm/min

Let

x

and

y

be the base and height of the rectangle.

x

=

0.5

cm is constant :. dx/dt=0#. Area of the rectangle

is

A

=

x

⋅

y

. Differentiating both sides we get

d

A

d

t

=

d

x

d

t

⋅

y

+

d

y

d

t

⋅

x

;

y

=

1.5

,

d

y

d

t

=

1.5

cm /min.

∴

d

A

d

t

=

0

⋅

1.5

+

1.5

⋅

0.5

=

0.75

sq.cm/min.

The area of the rectangle is changing at

0.75

sq.cm/min