A rectuangle is 14 cm long and 10 cm wide . If the length is reduces by x cm and its width is increade also by x cm so as to make a squre , then its area increased by-

Let's calculate the initial area of the rectangle:

Initial length = 14 cm Initial width = 10 cm

Initial area = length * width Initial area = 14 cm * 10 cm Initial area = 140 square cm

Now, we want to reduce the length by x cm and increase the width by x cm to make a square. After these changes, the dimensions of the square will be:

New length = 14 cm - x New width = 10 cm + x

To make a square, the new length and new width should be equal:

14 cm - x = 10 cm + x

Now, let's solve for x:

14 cm - x - 10 cm - x = 0 4 cm - 2x = 0 4 cm = 2x x = 2 cm

So, x is 2 cm.

Now, we can calculate the new area of the square:

New side (after changes) = 14 cm - 2 cm = 12 cm

New area = (New side)^2 New area = 12 cm * 12 cm New area = 144 square cm

To find the increase in area, subtract the initial area from the new area:

Increase in area = New area - Initial area Increase in area = 144 square cm - 140 square cm Increase in area = 4 square cm

So, the area is increased by 4 square cm.