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.
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%.
To find the percentage increase in the other side of the rectangle, we can use the concept of ratios.
Let's assume the original length of one side of the rectangle is L, and the original width (other side) is W.
Given that the area has increased by 5%, we can say:
New Area = Original Area + (5% of Original Area)
Since the area of a rectangle is given by Length x Width, the new area can be expressed as:
LW + 0.05(LW)
Simplifying this expression, we get:
(1 + 0.05)LW
To find the new length, we know it has been decreased by 10%. This means the new length can be expressed as:
New Length = Original Length - (10% of Original Length)
= L - 0.1L
= 0.9L
To find the new width (other side), we can divide the new area by the new length:
New Width = New Area / New Length
= (1 + 0.05)LW / 0.9L
= 1.05W / 0.9
To find the percentage increase in the width, we can compare the new width to the original width:
Increase in Width = ((New Width - Original Width) / Original Width) * 100
Let's calculate it:
Increase in Width = ((1.05W / 0.9 - W) / W) * 100
= (1.1667W - W) / W * 100
= 0.1667W / W * 100
= 16.67%
Therefore, the other side of the rectangle increased by approximately 16.67%.