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
IrinaK [193]
3 years ago
15

Two competitive neighbours build rectangular pools that cover the same area but are different shapes. Pool A has a width of (x +

3)m and a length that is 3m longer than its width. Pool B has a length that is double the width of Pool A. The width of Pool B is 4m shorter than its length.
a. Find the exact dimensions of each pool if their areas are the same.
b. Verify that the areas are the same.
Mathematics
1 answer:
GenaCL600 [577]3 years ago
5 0

<u>Answer: </u>

a)Dimensions of pool A are length = 6.667m and width = 3.667 m and dimension of pool B are length = 7.333m and width = 3.333m.

b) Area of pool A is equal to area of pool B equal to 24.44 meters.

<u> Solution: </u>

Let’s first calculate area of pool A .

Given that width of the pool A = (x+3)  

Length of the pool A is 3 meter longer than its width.

So length of pool A = (x+3) + 3 =(x + 6)

Area of rectangle = length x width

So area of pool A =(x+6) (x+3)        ------(1)

Let’s calculate area of pool B

Given that length of pool B is double of width of pool A.

So length of pool B = 2(x+3) =(2x + 6) m

Width of pool B is 4 meter shorter than its length,

So width of pool B = (2x +6 ) – 4 = 2x + 2

Area of rectangle = length x width

So area of pool B =(2x+6)(2x+2)        ------(2)

Since area of pool A is equal to area of pool B, so from equation (1) and (2)

(x+6) (x+3) =(2x+6) (2x+2)    

On solving above equation for x    

(x+6) (x+3) =2(x+3) (2x+2)  

x+6 = 4x + 4    

x-4x = 4 – 6

x = \frac{2}{3}

Dimension of pool A

Length = x+6 = (\frac{2}{3}) +6 = 6.667m

Width = x +3 = (\frac{2}{3}) +3 = 3.667m

Dimension of pool B

Length = 2x +6 = 2(\frac{2}{3}) + 6 = \frac{22}{3} = 7.333m

Width = 2x + 2 = 2(\frac{2}{3}) + 2 = \frac{10}{3} = 3.333m

Verifying the area:

Area of pool A = (\frac{20}{3}) x (\frac{11}{3}) = \frac{220}{9} = 24.44 meter

Area of pool B = (\frac{22}{3}) x (\frac{10}{3}) = \frac{220}{9} = 24.44 meter

Summarizing the results:

(a)Dimensions of pool A are length = 6.667m and width = 3.667 m and dimension of pool B are length = 7.333m and width = 3.333m.

(b)Area of pool A is equal to Area of pool B equal to 24.44 meters.

You might be interested in
Write an equation that is proportional.
maksim [4K]

Answer:Learn how to write a proportional equation y=kx where k is the so-called "constant of proportionality".

Step-by-step explanation:

https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-ratio-proportion/cc-7th-equations-of-proportional-relationships/v/equations-of-proportional-relationships#:~:text=Learn%20how%20to%20write%20a,called%20%22constant%20of%20proportionality%22.

5 0
3 years ago
i’m a little bit confused on this, so please answer showing the points i can plot on the graph! thanks!:)
Wewaii [24]

Answer:

Just a heads up, please google , desmos.com . ive been reccomending this to alot of people. it graphs everything for you while providing adequate reasoning and explanation.

7 0
2 years ago
Find the common ratio of the geometric sequence-15,-30,-60
blondinia [14]

Answer:

2

Step-by-step explanation:

The common ratio of the sequence is 2 because between each term you are multiplying by 2 to get the next term

7 0
3 years ago
Pam likes to practice dancing while preparing for a math tournament. She spends 80 minutes every day practicing dance and math.
Kisachek [45]
80/2= 20 then take away the extra 20 from the math for dance and you have the answer... 20 get it?
8 0
3 years ago
Read 2 more answers
If f(x) = 4x + 2, what is the value of f(3)? <br><br> O 8<br> O 14<br> O 45<br> O 66
lutik1710 [3]

Answer:

14

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • Answers are appreciated! :D
    15·1 answer
  • A partnership owned equally by 15 partners is worth $1.5 million. The partnership loses a lawsuit
    12·1 answer
  • What is the answer of 7/10x +4 &lt;49
    10·2 answers
  • An automotive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic. Step 1 of 2: Su
    5·1 answer
  • If 8 pigs can fit in a pen, how many pens are necessary to make sure 71 pigs are all in a pen?
    6·1 answer
  • a bag has 1 red marble, 4 blue marbles, and 3 green marbles. peter draws a marble randomly from the bag, replaces it, and then d
    8·1 answer
  • A line passes through the point (10,2) and has a slope of 1/2. Write an equation in slope-intercept form for this line.
    12·2 answers
  • If s(x) = 2 - x2 and t(x) = 3x, which value is equivalent to (st)(-7)
    10·1 answer
  • There will be 1,398 students attending the assembly. During the assembly, our principal is going to be passing out 4 pieces of p
    10·1 answer
  • 4. Is the relation represented on the graph a function? Explain
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!