Question

a rectangle width and length are 22 cm and 30 cm respectively if the length increases by 10% and the area is unchanged by what percentage does the width decrease

Answer 1

Answer:

Given, l= 30 cm

b= 22 cm

:. Area= l×b

=30×22 =660 cm

Now, Let new length be l'

l'= l + 10% of l

= 30 + 10/100 × 30

= 30 + 3

= 33 cm

So, l'×b' = 660

b'= 660/33 = 20 cm

b – x% of b = b'

22 – 22x% = 20

42 = 22x%

42/22 = x%

x% = 1.909090...%

Hence, by 1.909090... percentage the width decreases.

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Answer 2

Answer:

The width of a rectangle is decreased by 2%.

Step-by-step explanation:

Step 1 of 3

Given: The length of a rectangle = 30 cm

The width of a rectangle = 22 cm

Then,

The area of a rectangle = length $\times$ width

                                       = 30 × 22

                                       = 660 $cm^2$

Step 2 of 3

Since the length of a rectangle increases by 10%.

So, the new length of a rectangle = 30 + (10% of 30)

                                                         = 30 + $\left(\frac{10}{100}\times 30\right)$

                                                         = 30 + 3

                                                         = 33 cm

Let the new width of a rectangle be y.

According to the question,

The area of a rectangle remains unchanged, i.e.,

The area of a rectangle = new length × new width

⇒ 660 = 33 × y

⇒ y = 660/33

⇒ y = 20

Thus, the new width of a rectangle is 20 cm.

Step 3 of 3

The percentage decrease in the width is,

= (Original width - new width)%

= (22 - 20)%

= 2%

Therefore, the width of a rectangle is decreased by 2%.

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