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.
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