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
salantis [7]
3 years ago
13

A rectangle is twice twice as long as it is wide and has the same perimeter as a square whose area is 9 square feet feet larger

than that of the rectangle. what are the dimensions of both the rectangle and the​ square?
Mathematics
1 answer:
Alex_Xolod [135]3 years ago
8 0
If the width of the rectangle is w and the length is l, then l=2w (since the rectangle is twice as long as it is wide) and w*l=w*(2w), as well as 2w+2l being 2w+2(2w)=2w+4w=6w. Since the perimeter (2w+2l) is the same as the perimeter of the square (if one side length of the square is x, then the perimeter is 4x), 6w=4x and by dividing both sides by 4, we get 6w/4=x=3w/2. 
Since the area of the square is x^2, we can plug 3w/2 in for x to get
(3w/2)^2=9w^2/4 as the area of the square. Since the area of the square is 9 feet larger than the rectangle, 9w^2/4-9=2*l=w*(2w)=2w^2. Subtracting 2w^2 from both sides of 2w^2=9w^2/4-9 as well as adding 9 to both sides, we get w^2/4=9 and by multiplying 4 to both sides we get w^2=46 and by square rooting both sides we get w=sqrt(36)=6. Since the length is 2w, 6*2=12=the length. Since the area of the rectangle is l*w=6*12=72, the square's area is 9 more than that and is 72+9=81. Since x^2 is the area of the square which equals 81, 81=x^2 and by square rooting both sides we get x=9
You might be interested in
What equation represents the proportional relationship displayed in the table? x 2 4 6 8 y 10 20 30 40 Enter your answer by fill
hjlf

Answer: y=5x

Step-by-step explanation:

pls mark brainliest :)

5 0
2 years ago
What is the perimeter of this rectangle? *<br> 5 cm<br> 8 cm<br> ar swer
Tju [1.3M]

Answer:

Perimeter of rectangle = 2(l+b)

= 2(8+5)cm

= 2*13 cm

= 26cm

8 0
3 years ago
Simplify 2(10−x)+3(12−x)
GarryVolchara [31]

Answer:

-5x + 56

Step-by-step explanation:

Use distributive property to refine.

20 - 2x + 36 - 3x

Combine Like Terms

-5x + 56

3 0
3 years ago
Read 2 more answers
Find the equation of plane that contains P(1,-1,2) and has the normal n=2i+3j+5k (please answer quickly )
mixas84 [53]

Answer:

2x + 3y + 5z = 9

Step-by-step explanation:

The normal defines all the planes perpendicular to that vector. To isolate to a single plane, just apply the known point.

ax + by + cz = d

2x + 3y + 5z = d

2(1) + 3(-1) + 5(2) = 9

8 0
3 years ago
Rusty's hair grows at the rate of 1 over 4 inches per month.
vichka [17]
1/4 = 2/8. Remember that. This means that 1/8 is equal to half of a month. It there is 5/8, you can add a half month for every eight. In this case, it will take 2 and a half months


Hope this helped!!!!
4 0
3 years ago
Read 2 more answers
Other questions:
  • What is the vertex of the graph of y = −1(x − 2)2 + 3
    9·1 answer
  • Please help:<br><br> 3/4 of 24 cm
    15·2 answers
  • Is 0.7105386266520861 a rational or irrational number?
    6·2 answers
  • liz wants to buy her favorite musical group’s new cd. the cd costs $15.24, including tax. liz gives the store clerk a twenty-dol
    14·1 answer
  • 4.1g + 8= 1.1g + 14 what is g?
    13·2 answers
  • The equation x^2-9=0 has how many real solutions
    15·1 answer
  • An item has a listed price of $80. If the sales tax rate is 7%, how much is the sales tax (in dollars)
    5·1 answer
  • Ndicate the answer choice that best completes the statement or answers the question.
    7·1 answer
  • Divide ₹210 among A and B in the ratio 2:3​
    14·2 answers
  • The width of a rectangular field is 20 feet less than its length. the area of the field is 12,000 ft2. what is the length of the
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!