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
Someone please help I'm so stuck
Trava [24]
The picture won't load, but I would surely help!
7 0
3 years ago
How many edges does a rectangle prism have?
creativ13 [48]

the answer to your question there would be 12

4 0
3 years ago
Read 2 more answers
Solve for x<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B4x%20-%206%7D%7B4%7D%20%20%3D%20%20%5Cfrac%7B2x%20%2B%205%7D%7B3%7
Marizza181 [45]

Answer:

x = 9.5

Step-by-step explanation:

Given

\frac{4x-6}{4} = \frac{2x+5}{3} ( cross- multiply )

3(4x - 6) = 4(2x + 5) ← distribute parenthesis on both sides

12x - 18 = 8x + 20 ( subtract 8x from both sides )

4x - 18 = 20 ( add 18 to both sides )

4x = 38 ( divide both sides by 4 )

x = \frac{38}{4} = 9.5

6 0
3 years ago
Please explain! Math​
Nana76 [90]
I believe (-2,2) or (2,3)
6 0
2 years ago
What is the coefficient of the variable 2q + 24
Rudik [331]

Answer:

2

Step-by-step explanation:

The coefficient is the number before the variable. Therefore 2 is the coefficient of variable q.

6 0
2 years ago
Other questions:
  • What is time-and-a-half for $7.51?
    6·1 answer
  • How do you write the sum of 17 and a number in algebraic expression
    5·1 answer
  • A study is designed to determine whether grades in a statistics course could be improved by offering special review material. Th
    7·1 answer
  • What is the inverse of -2
    11·1 answer
  • What is the volume, in cubic units, of a pyramid of height 8 and a
    5·2 answers
  • How do i write seven thousand, two hundred fifty-six and thirty-five hundredths in expanded form
    9·2 answers
  • Select all the points that are on the graph of the line 3x+2y=24
    10·1 answer
  • Name 3 pairs of adjacent angles and 3 pairs of vertical angles.​
    5·1 answer
  • Jing has $800 to deposit into two different savings account. She will deposit $600 into an account that earns simple interest an
    15·1 answer
  • Whats (x + 3) - (5x - 4)
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!