# Homework Help: What fraction has the length of the rectangle been reduced?

1. Jul 17, 2017

### Natasha1

1. The problem statement, all variables and given/known data
The width of a rectangle is increased by one tenth, but the area remains the same. By what fraction has the length of the rectangle been reduced?

3. The attempt at a solution
Length = x
Width = x + 1/10

Set equation:
L * W
x *(10x + x)
10x^2 + x^2

2. Jul 17, 2017

### mjc123

Why do you assume the length and width are initially equal? What is the width after increasing (It is not x + 1/10).
Try writing Before: length = L, width = W. After: length = Lx, width = Wy where x and y are constants. What is y? Therefore what is x?

3. Jul 17, 2017

### Natasha1

Length = L*x
Width = W*y
where x and y are constants

W*(1/10) and L*x

4. Jul 17, 2017

### scottdave

I interpret as "the width is increased by 1/10 (of the original width)" or New_Width = Old_Width + Old_Width*(1/10)
I believe this is how the problem intends. Keep the area constant (set the new area equal to original).

5. Jul 17, 2017

### Natasha1

original dimensions ---- w by l
original area = wl

new width = 9w/10
new length = L
L(9w/10) = lw
L = lw/(9w/10) = (10/9)l = 1.111..
so the length would have to increase which does not make sense as it says reduce in question.
The increase is 10/9 of the original or appr 11.1%

6. Jul 17, 2017

### scottdave

It looks like you are on the right track with the formulas, but you have the new width less than the original, while the problem states that it was increased.

7. Jul 17, 2017

### Natasha1

new width = w + w/10
new length = L
L(11w/10) = lw
L = lw/(11w/10) = (10/11)l = 0.90909....
so the length would have to increase by 10/11 of the original or appr 9.09%

8. Jul 17, 2017

### scottdave

Since area is constant, if one dimension increases what happens to the other one? Think in extremes. If one dimension doubles, what happens to the other one?

9. Jul 17, 2017

### Natasha1

so the length would have to decrease by 10/11 of the original or appr 9.09%