In a rectangle the length is increased by of the original length. by what proportion should the width be reduced so that the area will be the same?
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If length is increased by x times then width should be reduced by x times so as the area remains the same.
If length is increased by x times then width should be reduced by x times so as the area remains the same.
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Given: In a rectangle the length is increased by of the original length.
To find: The proportion with which the width should be reduced so that the area will be the same.
Solution:
Let the length be increased by x. The area of a rectangle is calculated by the following formula.
Here, A is the original area of the rectangle, l is the length and w is the width. Now, if the length was increased by x and the area remained the same, the equation can be written as follows.
Here, w' is the new width.
Therefore, the proportion with which the width should be reduced so that the area will be the same is A/(l+x).
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