Question

A rectangle's 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?
22​

Answer 1

Step-by-step explanation:

Given:

• The length and the width of a rectangle is 30 cm and 22 cm.
• Next, the length is increased by 10%. So, now the length is => 30×1100/100 cm = 33 cm.
• The area remains unchanged.

Solution:

• The area of the rectangle is => (30×22) cm² = 660 cm².
• Now, let the decreased width be x.

So, 33×x = 660 (given that the area will be same)

=> x = 660/33

=> x = 20

Now, the width is decreased by (22–20) cm = 2 cm.

Or, the width is decreased by

(2/22)×100%

$= 9 \times \frac{1}{11} \%$

Answer 2

Answer:

Percentage decrease in width = 9.09%

Step-by-step explanation:

Given,

The length and width of the rectangle are 22 and 30 cm

Area remains the same when the length is increased by 10%

To find,

The percentage increase in the width

Solution:

The area of the rectangle = l ×b, where 'l' is the length and 'b' is the breadth of the rectangle

Percentage in decrease = $\frac{decrease}{Original \ value } X100$

Solution:

Let l and b be the length and width of the rectangle

Let l₁ and b₁ be the length and width after the change.

Then we have,

l = 22, b = 30

Since the length increased by 10%,  we get

l₁ =  l₁ + 10% l₁ = 22 + 10%22 = 22 + 2.2 = 24.2cm

∴ l₁ = 24.2cm

Since it is given that the area remains the same after the change we have

l ×b = l₁ × b₁ ---------------(1)

Substituting the values of l,b, l₁ in equation (1) we get

22 ×30  = 24.2 × b₁

660 = 24.2 × b₁

b₁ = 27.2727

Decrease in width = 30 -  27.2727 = 2.7272

Percentage in decrease = $\frac{decrease}{Original \ value } X100$

= $\frac{2.7272}{30} X100$

= 9.09%

Answer:

Percentage decrease in width = 9.09%

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