the area of a rectangle has increased by 5%. The length of one side was decreased by 10%. By what percentage was the other side increased? give yoour answer correcr to the nearest integer.

Answer 1

Let's assume the original length of the rectangle is x and the original width is y.

The area of the original rectangle is given by A1 = xy.

After the area increases by 5%, the new area is A2 = 1.05xy.

Also, the length of one side (let's say the length) decreases by 10%, making it 0.9x.

The new width, w2, can be found using the formula: (w2)(0.9x) = 1.05xy.
Dividing both sides by 0.9x, we get:
w2 = (1.05xy) / (0.9x) = 1.1667y.

Therefore, the new width of the rectangle is approximately 1.1667 times the original width.

To find the percentage increase, we calculate: (1.1667y - y) / y * 100%.

Simplifying, we get: 0.1667 * 100% = 16.67%.

Therefore, the other side was increased by approximately 17%.