What fraction has the length of the rectangle been reduced?

In summary, the width of a rectangle is increased by 1/10, while keeping the area constant. This means that the length of the rectangle would need to decrease by 10/11 of the original length, or approximately 9.09%, in order to maintain the same area.
  • #1
Natasha1
493
9

Homework Statement


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?

The Attempt at a Solution


Length = x
Width = x + 1/10

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

I am stuck... Please help...
 
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  • #2
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
Length = L*x
Width = W*y
where x and y are constants

W*(1/10) and L*x
 
  • #4
When i read this:
Natasha1 said:
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?
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).
 
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  • #5
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
Natasha1 said:
original dimensions ---- w by l
original area = wl

new width = 9w/10

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.
 
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  • #7
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%

Is this correct please?
 
  • #8
Your numerical answer is correct, but the conclusion is not.
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
so the length would have to decrease by 10/11 of the original or appr 9.09%
 

1. What is a fraction?

A fraction is a mathematical term used to represent a part of a whole. It consists of a numerator (the number on top) and a denominator (the number on the bottom), separated by a horizontal line. For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator. Fractions can also be written in decimal form, such as 0.75, where the numerator is divided by the denominator.

2. How do you calculate the length of a rectangle?

To calculate the length of a rectangle, you need to know the measurement of its width and its area. The formula for finding the length of a rectangle is length = area / width. For example, if a rectangle has an area of 24 square units and a width of 6 units, its length would be 24/6 = 4 units.

3. What does it mean for a fraction to be reduced?

A fraction is considered to be reduced when its numerator and denominator have no common factors (other than 1). This means that the fraction cannot be simplified any further. For example, the fraction 4/8 can be reduced to 1/2 because both 4 and 8 can be divided by 4. However, the fraction 3/5 is already reduced because 3 and 5 do not have any common factors.

4. How do you reduce a fraction?

To reduce a fraction, you need to find the greatest common factor (GCF) of its numerator and denominator and then divide both the numerator and denominator by the GCF. The resulting fraction will be in its reduced form. For example, to reduce the fraction 12/18, you need to find the GCF of 12 and 18, which is 6. Dividing both 12 and 18 by 6 gives the reduced fraction of 2/3.

5. Why is it important to reduce fractions?

Reducing fractions is important because it makes them easier to work with and compare. It also helps to simplify calculations and makes the answer more precise. In addition, reduced fractions are often used in real-life situations, such as cooking or measuring, where precise measurements are necessary.

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