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
Ne4ueva [31]
3 years ago
10

The distance from one corner of a rectangular garden to the other is 13 ft. The length of the garden is 7 ft longer than the wid

th. Write a quadratic equation to find the dimension of the garden. Solve the equation and find the area of the garden in square feet.
Mathematics
1 answer:
coldgirl [10]3 years ago
4 0

Answer:

  • dimensions: 12 ft by 5 ft
  • area: 60 ft²

Step-by-step explanation:

Let x represent the shorter dimension in feet. Then the longer one is x+7 and the Pythagorean theorem tells us the relation of these to the diagonal is ...

  x² + (x+7)² = 13²

  2x² +14x + 49 = 169 . . . . eliminate parentheses

  x² +7x -60 = 0 . . . . . subtract 169 and divide by 2

  (x +12)(x -5) = 0 . . . . factor the equation

  x = -12 or +5 . . . . . . . only the positive value of x is useful here.

The short dimension is 5 ft, so the long dimension is 12 ft. The area is their product, 60 ft².

_____

<em>Comment on finding the area</em>

The quadratic equation above can be rearranged and factored as ...

  x(x +7) = 60

Since the dimensions of the garden are x and (x+7), this product is the garden's area. This equation tells us the area is 60. We don't actually have to find the dimensions.

You might be interested in
38 is what percent of 40?
guapka [62]
38 divided by 40, then multiply by 100 = 95%
4 0
2 years ago
Read 2 more answers
Which expression represents the sum (3z−11)+(6−6z) ?
Fudgin [204]

Answer: z = -5/-3

Step-by-step explanation:

(3z−11)+(6−6z)

3z - 11 + 6 - 6z

- 6z + 3z - 11 + 6

- 3z - 5

z = -5/-3

6 0
3 years ago
Evaluate: 54-75+81-(-27)+53
romanna [79]

Hi the answer is 344

4 0
3 years ago
Read 2 more answers
It costs $2.50 to rent a pair of bowling shoes and $1.75 for each game bowled.
garri49 [273]
I think it would be $77.00
3 0
3 years ago
I GIVEEEE BRAINLILSTT
Zigmanuir [339]
Alr bet x + 8 y - 9 :)
6 0
2 years ago
Other questions:
  • On Monday Charlie earned $16 for 2 hours of babysitting. Getting paid the same rate he earned $40 for babysitting on Saturday Ho
    10·2 answers
  • How does a digit in the ten thousands place to a digit in the thousand place?
    7·2 answers
  • An ellipse has vertices of (5, 0) and (–5, 0) and covertices of (0, 2) and (0, –2). Use the given information to answer the ques
    6·1 answer
  • Which of the following input-output tables represents the function graphed below?
    13·1 answer
  • Can 9,999,999 have the same value
    5·1 answer
  • The answers for the tables
    6·1 answer
  • What do you call the two numbers, when multiplied together, results in the product of 1?
    9·2 answers
  • Please explain this to me and say the answer!! ASAP!!!
    14·1 answer
  • Help with a problem!!!
    12·2 answers
  • PLS ANSWER IT PLS PLS
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!