The length of a rectangle is increased by 50%. By what percent would the width be increased to keep the same area?
a.43/3
b.45/4
c.33-1/3
d.31-1/3
length is 3/2
so, width is 2/3
sorry but i don't get it
so, if the dimensions are x and y,
50% increase of y is 1.5y. But, you want the new area to be the same. So, if x is multiplied by k, you want
(k)(x)(3/2)(y) = xy
(k)(3/2)(xy) = xy
k(3/2) = 1
k = 2/3
So, if the new width is 2/3 of the old width, that is a decrease of 1/3, or 33-1/3 %
what is k by the way?
do you actually read what I write? I explained k, and I used it. Don't make me do your thinking as well as your math!
To determine the percent increase in width, we need to consider the changes in length and area of the rectangle.
1. Let's start by assuming the original length of the rectangle is L and the original width is W.
2. The area of the rectangle is then given by A = L * W.
3. If the length is increased by 50%, then the new length would be 1.5 times the original length, or 1.5L.
4. Since the area is invariant, the new area would still be A, but with the updated dimensions: A = (1.5L) * W.
5. To find the new width, we can rearrange the equation as follows: Wnew = A / (1.5L).
6. Notice that Wnew = A / (1.5L) is equivalent to Wnew = (1/1.5) * (A / L).
7. Simplifying further, we get Wnew = (2/3) * (A / L) = (2/3) * W.
Now, to calculate the percent increase in width, we compare the change in width to the original width:
Change in width = Wnew - W
Percent increase in width = (Change in width / Original width) * 100
Substituting the values we found:
Change in width = (2/3) * W - W = (2W - 3W) / 3 = -W / 3
Percent increase in width = (-W / 3) / W * 100 = -100/3 ≈ -33.33 ≈ -33-1/3
Therefore, the percent increase in width to keep the same area when the length is increased by 50% is approximately 33-1/3.
The correct option is c. 33-1/3.