Question

A square plate is contracting at the rate of 4 2⁄. Find the rate of decrease of perimeter when the side of the square is 14 cm.

Answer 1

Answer:

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>>A square plate is contracting at the uni

Question

A square plate is contracting at the uniform rate of 2cm

2

/sec. Find the rate of decrease of its perimeter when the side of the square is 16 cm long.

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Solution

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Given:Let x be the side of the square plate and A be the area of the square plate

Given:

dt

dA

=−2 and x=16cm

A=x

2

⇒

dt

dA

=2x

dt

dx

⇒−2=2x

dt

dx

⇒

dt

dx

=

x

−1

=

16

−1

Let P be the perimeter then P=4x

dt

dP

=4

dt

dx

=4×

16

−1

=−0.22

∴ the perimeter of the square plate decreasing ar the rate of

4

1

cm\sec.

Answer 2

Answer: Rate of decrease of perimeter = $\bold{\frac{4}{7}\ cm/s}$

Given: Rate of contraction = $4\ cm^2/s$.

To Find: Rate of decrease of perimeter.

Step-by-step explanation:

Step 1: Since a square has four equal sides and four equal angles, it is a regular quadrilateral.

An amount, frequency, or measure that is often compared to another quantity or measure known as rate of that quantity.

Let the side of square is x cm. Then area of the square is $x^2$.

Step 2: Rate of contraction is

$\frac{dA}{dt}= 4 cm^2/s \\\\\frac{dA}{dt}= \frac{dx^2}{dt}=2x\frac{dx}{dt}\\\\2x\frac{dx}{dt}=4\\\\\frac{dx}{dt}=\frac{2}{x} \\\\\frac{dx}{dt}=\frac{2}{14}=\frac{1}{7}$

Step 3: The complete length of a shape's border is referred to as the perimeter in geometry. A shape's perimeter is calculated by summing the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

Perimeter of the square (P) = $4\times x=4x$

Now, rate of decrease of perimeter is

 $\frac{dP}{dt}= \frac{d(4x)}{dt}\\\\\frac{dP}{dt}= 4\frac{dx}{dt}\\\\\frac{dP}{dt}= 4\times \frac{1}{7}=\frac{4}{7}$

Hence, we can say that the rate of decrease of perimeter = $\frac{4}{7}\ cm/s$

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