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1 . A rectangle is 14 cm long and 10 cm wide. If the length is reduced by x cms and its width is increased also x cms so as to make it a square, then its area changes by:

A. 4
B. 144
C. 12
D. 2

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Answer: Option A

Explanation:

Let's call the new length of the rectangle "L" after reducing the length by x cm and increasing the width by x cm. Then, the new width of the rectangle would be "W".

We know that the original length of the rectangle was 14 cm and the original width was 10 cm, so we can write the following equations:

L = 14 - x
W = 10 + x

To make the rectangle into a square, the length and the width must be equal, so we can set L = W:

14 - x = 10 + x
24 = 20
x = 2

Now that we know x = 2, we can use that to find the new length and width of the rectangle:

L = 14 - 2 = 12
W = 10 + 2 = 12

The area of the original rectangle was 14 cm * 10 cm = 140 sq cm. The area of the new square is 12 cm * 12 cm = 144 sq cm. The difference between the two is 144 - 140 = 4 sq cm.

So, the area changes by 4 sq cm when the rectangle is transformed into a square.

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