What fraction has the length of the rectangle been reduced?

Click For Summary
SUMMARY

The problem discusses a rectangle where the width is increased by one-tenth while maintaining the same area. The original width is denoted as W, and the new width becomes 11W/10. Consequently, the length must decrease to maintain the area, resulting in a new length of 10/11L, which indicates a reduction of approximately 9.09% from the original length. This conclusion is reached by setting the original area equal to the new area and solving for the dimensions.

PREREQUISITES
  • Understanding of basic algebraic equations
  • Knowledge of area calculations for rectangles
  • Familiarity with fractions and percentages
  • Ability to manipulate variables in equations
NEXT STEPS
  • Study the relationship between dimensions and area in geometric shapes
  • Learn about the impact of changing one dimension on the others in fixed-area problems
  • Explore algebraic manipulation techniques for solving equations
  • Practice problems involving area conservation in rectangles and other shapes
USEFUL FOR

Students studying geometry, educators teaching algebraic concepts, and anyone interested in understanding the relationship between dimensions and area in geometric figures.

Natasha1
Messages
494
Reaction score
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...
 
Physics news on Phys.org
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?
 
Length = L*x
Width = W*y
where x and y are constants

W*(1/10) and L*x
 
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).
 
  • Like
Likes   Reactions: Buffu and SammyS
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%
 
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.
 
  • Like
Likes   Reactions: 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%

Is this correct please?
 
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?
 
so the length would have to decrease by 10/11 of the original or appr 9.09%
 

Similar threads

A+b=236, What numbers to get a maximum product ab?
  • · Replies 21 ·
Replies
21
Views
3K
Finding the Side-lengths of a Rectangle with Given Area Increase
  • · Replies 2 ·
Replies
2
Views
2K
What is the perimeter of a rectangle with a 3:2 ratio and an area of 294 dm2?
  • · Replies 5 ·
Replies
5
Views
2K
Calculating the Area of Rectangles: Solving for Unknown Side Lengths
  • · Replies 26 ·
Replies
26
Views
3K
How Do You Calculate the Total Area of Rectangles and Triangles Combined?
  • · Replies 3 ·
Replies
3
Views
2K
Minimum of x+1/x (Perimeter Square < Perim equal area rects)
  • · Replies 1 ·
Replies
1
Views
2K
How to solve a geometry problem involving concentric rectangles?
  • · Replies 8 ·
Replies
8
Views
3K
Finding the length and width of rectangle
  • · Replies 8 ·
Replies
8
Views
3K
Reducing one algebraic fraction to another
  • · Replies 3 ·
Replies
3
Views
2K
Find a line in the rectangle from 0.0 to some point
  • · Replies 4 ·
Replies
4
Views
2K