1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Burka [1]
1 year ago
14

1. Charlene wants to center a rectangular pool in her backyard so that the edges of the pool are an equal distance from the edge

s of the yard on all sides. The yard currently measures 60 m by 50 m. She wants to use ½ of the area of the yard for the pool. Create an equation for the pool’s dimensions and solve for the distance the pool is from the edge of the yard. Round your final answer to the nearest tenth of a meter.
Mathematics
1 answer:
Inga [223]1 year ago
5 0

First, we have to calculate the length of the sides of the pool, we are told that the scale factor of the backyard to the pool size equals 1/2, then we can find the length of the sides of the pool by multiplying the lengths of the sides of the backyard by 1/2, like this:

length of the pool = length of the yard * 1/2

width of the pool = width of the yard * 1/2

By replacing the 60 m for the length of the yard and 50 m for the width, we get:

length of the pool = 60 * 1/2 = 30

width of the pool = 50 * 1/2 = 25

Let's call x1 to the distance from the base of the pool to the bottom side of the yard and x2 to the distance from the top side of the pool to the top side of the yard, then we can formulate the following equation:

width of the yard = width of the pool + x1 + x2

Since we want the edges to be at an equal distance, x1 and x2 are the same, then we can rewrite them as x:

width of the yard = width of the pool + x + x

width of the yard = width of the pool + 2x

Replacing the known values:

60 = 30 + 2x

From this equation, we can solve for x to get:

60 - 30 = 30 - 30 + 2x

30 = 2x

30/2 = 2x/2

15 = x

x = 15

Now, let's call y1 to the distance from the right side of the corresponding side of the yard and y2 to the distance from the left side of the pool to the left side of the yard, with this, we can formulate the following equation:

length of the yard = length of the pool + y1 + y2

Since we want the edges to be at an equal distance, y1 and y2 are the same, then we can rewrite them as y:

length of the yard = length of the pool + y + y

length of the yard = length of the pool + 2y

Replacing the known values:

50 = 25 + 2y

50 - 25 = 25 - 25 + 2y

25 = 2y

25/2 = 2y/2

12.5 = y

y = 12.5

Now, we know that the pool must be at a distance of 15 m from the horizontal sides of the pool to the horizontal sides of the yard and that it must be at a distance of 12.5 m from the vertical sides of the pool to the vertical sides of the yards.

Here is a figure that depicts the results:

You might be interested in
Help what is 2v+5(3v+4
Artemon [7]

explanation:

There isn't an exact way to answer this problem. Is there more to the question? If not, I am unable to answer it for you.

4 0
2 years ago
Mason and Laney run laps. The ratio of the number of laps Mason ran to the number Laney ran was 2:3.
3241004551 [841]

Using proportions, it is found that Mason ran 620 meters.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Considering the ratio, the <em>rule of three</em> is given as follows:

2 laps for Mason - 3 laps for Laney.

n meters for Mason - 930 meters for Mason.

Applying cross multiplication:

3n = 930 x 2

n = 930 x 2/3

n = 620

Mason ran 620 meters.

More can be learned about proportions at brainly.com/question/24372153

#SPJ1

3 0
2 years ago
True or False? <br><br> Set A = { X | X is an even whole number between 0 and 2} = ∅
N76 [4]
It is false because 0and 2 and the middle number will be 1

7 0
3 years ago
Read 2 more answers
Whats 5 plus 73 pls help someone
trasher [3.6K]
78 is your answer............
8 0
3 years ago
Read 2 more answers
Fill in the blank. In the triangle below x = ______. Round your answer to two decimal places.
kirill [66]
Tan42°=x/35

x=35tan42°  units

x≈31.51 units (to nearest hundredth of a unit)
5 0
3 years ago
Read 2 more answers
Other questions:
  • The vertex of the parabola is at (-3,-2) which of the following could be its equation
    10·2 answers
  • Solve for x<br> 3/4x = -9
    10·2 answers
  • P(7, 10) and Q(9, 6) are the endpoints of a line segment. What is the midpoint M of that line segment?
    5·1 answer
  • If the ratio of the measure of the complement of an angle to the measure of its supplement is 1:3, find the measure of the angle
    14·1 answer
  • Find the missing side length in the image attached.
    13·2 answers
  • Which best describes the triangle or triangles, if any, that can be formed with sides
    12·1 answer
  • A system of two linear equations in which the lines are identical is classified as __________.
    9·2 answers
  • At 2:00 PM a car's speedometer reads 30 mi/h. At 2:20 PM it reads 50 mi/h. Show that at some time between 2:00 and 2:20 the acce
    10·1 answer
  • Can someone help me ??
    6·1 answer
  • Put the following equation of a line into slope intercept form, simplifying all fractions. 8x+10y=-30
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!