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
11111nata11111 [884]
3 years ago
9

How do you solve this?

Mathematics
1 answer:
puteri [66]3 years ago
7 0

Answer:

Width: 7

Length: 14

Step-by-step explanation:

The area of a rectangle can be found my multiplying the length by the width. We do not know neither the length nor the width. However, we do know that the length is 7 feet longer than the width. Because we do not know the value of either side, let's let x represent the width.

Since the length is 7 feet longer, we can represent the length by x+7.

Now that we have our values for the length and the width we can multiply them together to find our area.

(x)(x+7)=x^{2} +7x

Now we have our equation, so we can address the changes made by the original question. The original question states that when 7 is added to both the length and width the area becomes 3 times larger. To do so simply increase each side by 7 by adding 7 to the original values.

(x+7)(x+14)

And multiply our area by 3.

3(x^{2} +7x)

set these equal to each other to find your new equation.

(x+7)(x+14)=3(x^{2} +7x)

Now you need to solve for x. To do this first muliply (x+7) and (x+14).

(x+7)(x+14)=\\x^{2} +14x+7x+98=\\x^{2} +21x+98

Then multiply 3(x^{2} +7x)

3(x^{2} +7x)=\\3x^{2} +21x

Now you can begin solving for x.

x^{2} +21x+98=3x^{2} +21x

Subtract x^{2} from both sides.

21x+98=2x^{2} +21x

Subtract 21x from both sides.

98=2x^{2}

Divide by 2.

49=x^{2}

And finally take the sqaure root of both sides.

\sqrt{x^{2} }=\sqrt{49}\\x=7

Remember, because we are dealing with length, there cannot be negative. So while normally we would get both +7 <em>and</em> -7, in this case we <em>only </em>get +7.

Now that we have the value of x, we can plug it into our original values.

For width we simply get 7.

For length we get 7+7=14

To check our answer we cna multiply 7 by 14 to get 98. Then we can add 7 to our length and width to get 14 and 21. Multiply these together and we get 294. 294 divided by 3 is 98, proving our answer correct.

You might be interested in
the width of a rectangle is the length minus 2 units. The area of the rectangle is48 units. What is the width, in units, of the
tatuchka [14]

Answer:

6

Step-by-step explanation:

put unknown as y

area of rectangle = width × long

y(y - 2)=48

y² -2y =48

u can use scientific calculator to find this

y²-2y-48=0

(y-8)(y+6)=0

y=8 y=-6

take the positive value and ignore the negative value

width=y-2 long=8

8-2=6

I hope this help you :)

6 0
3 years ago
Please help I need it for today
s2008m [1.1K]

Step-by-step explanation:

Disculpe pero de qué grado es usted para ayudarle un poquito más mejor

8 0
2 years ago
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS PLEASE AND PLEASE EXPLAIN WHY THAT IS THE ANSWER
melamori03 [73]

Answer: 5x 5y

Step-by-step explanation: because of the length

4 0
2 years ago
Can you form a right triangle with the three lengths given? Why or why not? 4mi, 5mi, 6mi
Vladimir [108]
A right triangle must satisfy this equation: a^2 + b^2 = c^2 

a= shortest length
b=medium length
c=the longest length

a triangle with sides 4,5,6 will satisfy not this equation because:
4^2 + 5^2 ≠ 6^2 
16+25 = 41

41 ≠ 36

so the answer is C.

Hope this helps.

-Jabba

6 0
3 years ago
Read 2 more answers
Solve for y. <br> 2x+6y=12
Veronika [31]
2x + 6y = 12

2x - 2x + 6y = 12 - 2x

6y = 12 - 2x

6y/6 = 12/6 - 2x/6

Y = 2 - 2/6 X

Y = 2 - 1/3 X or

Y = -1/3 X + 2.
7 0
3 years ago
Other questions:
  • Sabena invests $250 in an account that earns 2.4% interest per year compounded continuously. How many years will it take the acc
    13·1 answer
  • Write the augmented matrix for each system of equations.
    10·1 answer
  • What is 7/4 as a mixed number?
    14·2 answers
  • PLEASE HELP with math
    10·1 answer
  • Alegbra, K12 Question. Answer needed ASAP --- Brainliest to the correct answer!
    14·1 answer
  • Howww???? <br> Answer??????
    5·2 answers
  • In a hostel of 50 students there is food for 40 days.If 30 more students join the hostel then how long will the food last? 23 da
    14·1 answer
  • 70% of 120 = 120x70/100 <br> How do you figure this out
    6·1 answer
  • Two rectangles are similar. The first rectangle has a length of 15 cm and a width of 10 cm. The width of the second rectangle is
    5·1 answer
  • Which of the following sets of numbers could not represent the three sides of a triangle?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!