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
egoroff_w [7]
2 years ago
7

A walkway is being installed around a rectangular playground. The playground is 30 feet by 12 feet, and the total area of the pl

ayground and the walkway is 1,288 ft^2. What is the width of the walkway?
Mathematics
2 answers:
Lelechka [254]2 years ago
7 0

Answer: the width of the walkway is 8 feet.

Step-by-step explanation:

Let x represent the width of the walkway.

If the length of the playground is 30 feet, then the total length of the playground and the walkway is 30 + x + x = 30 + 2x

If the width of the playground is 12 feet, then the total width of the playground and the walkway is 12 + x + x = 12 + 2x

If the total area of the playground and the walkway is 1,288 ft^2, it means that

(30 + 2x)(12 + 2x) = 1288

360 + 60x + 24x + 4x² = 1288

4x² + 84x + 360 - 1288 = 0

4x² + 84x - 928 = 0

Dividing through by 4, it becomes

x² + 21x - 232 = 0

x² + 29x - 8x - 232 = 0

x(x + 29) - 8(x + 29) = 0

x - 8 = 0 or x + 29 = 0

x = 8 or x = x = - 29

Since the width of the walkway cannot be negative, then x = 8

worty [1.4K]2 years ago
4 0

Answer:

10.3

Step-by-step explanation:

From these question, we can illustrate the playground has a small rectangle with 30x12ft

the walkway is around it with an area of 1288ft²

the playground area = 30 x 12 = 360ft²

the length dimension of the walkway is 30+y+y( these is because the walkway is round the playground in two sides) = 30 +2y

the breadth dimension of the walkway is 12+y+y ( these is because the walkway is round the playground in two sides) = 12+2y

Area of walkway = (30+2y)(12+2y)= 30(12+2y)+2y(12+2y) = 360+60y+24y+4y²= 360+84y+4y²

The total area = 1288ft²

The total area = area of walkway - area of playground

1288ft² = 360+84y+4y² - 360

choose like terms

1288 = 360-360+84y+4y²

1288 = 84y+4y²

divide by 4

322= 21y+y²

y²+21y-322 =0

using quadratic formula

x= (-b±√b²-4ac)/2a = {-21±√21²-4(1)(-322)}/2x1 =  {-21±√441+1288}/2x1  = -21±√1729/2

-21+√1729/2   -21-√1729/2

√1729 = 41.5812457726

-21+√1729/2   -21-√1729/2

{-21+41.5812457726}/2   {-21-41.5812457726}/2

20.5812457726/2          -62.5812457726/2

10.2906228863              -31.2906228863

we disregard the negative sign

our width is 10.2906228863 ≅10.3

You might be interested in
Find the values of the variables.
iris [78.8K]

Answer:

x=-1/2

Step-by-step explanation:

2x+2=4x+3

-1=2x

x=-1/2

3 0
2 years ago
Solve 2x+y=3 x+y=5 in substitution method
Nastasia [14]
2x+y=3
- x+y=5
---------------
x=-2

2(-2)+y=3
y=7

-2+y=5
y=7

(-2,7)
4 0
3 years ago
Bob is trying to decide between two cell phone plans. Plan A has no flat fee, but the user must pay $10 cents per minute on the
professor190 [17]
$ per min is a rate. you multiple by minutes to get dollars.

A = 10x
B = 5x + 20

set them equal to find minutes, x.

10x = 5x + 20
10x - 5x = 20
5x = 20

x = 4
4 0
3 years ago
Read 2 more answers
Help help help help me pls !,!,!,
Len [333]

Answer:

96

Step-by-step explanation:

First, you find the area of RPQ using 1/2×base×height. That is, 1/2×6×8. And the answer is 24. Then you multiply 24 by 4 to get the area of all the sides excluding the base to get 96.

8 0
3 years ago
Find the measure of b. (Explain how you found it please!)
Allisa [31]

Answer:

125 deg

Step-by-step explanation:

Keep these three rules in mind:

1) A central angle (vertex is the center of the circle) has the same measure as the arc it intercepts.

2) The measure of an inscribed angle (vertex is point on circle) is half the measure of the intercepted arc.

3) Opposite angles of a rectangle inscribed in a circle are supplementary.

110 deg is a central angle.

By rule 1), the arc intercepted by the central angle 110 deg also measures 110 deg.

a is an inscribed angle that intercepts an arc of 110 deg.

By rule 2), the measure of an inscribed angle is half the measure of the intercepted arc.

angle a measures 55 deg.

Rule 3) Angles a and b are supplementary.

a + b = 180

55 + b = 180

b = 125

5 0
2 years ago
Other questions:
  • On a test flight during the landing of the space shuttle the ship was 323 ft above the end of the landing strip. If it came in a
    9·1 answer
  • What is the answer to this problem
    14·2 answers
  • Based on his salary, Kevin knows that he will have $336.00 withheld from his paycheck for federal income tax. He would like to h
    8·2 answers
  • Explain a strategy you could use to compare 2/6 and 5/8
    11·1 answer
  • Find f'(a). f(x)=<img src="https://tex.z-dn.net/?f=%5Csqrt%7B2-2x%7D" id="TexFormula1" title="\sqrt{2-2x}" alt="\sqrt{2-2x}" ali
    13·1 answer
  • There are 4 circles and 2 squares. What is the simplest ratio of squares to circles?
    7·1 answer
  • The Pythagorean triple (5, 12, 13) can't be generated from the identity (x? 1)2 + (2x)2 = (x2 + 1)
    13·1 answer
  •  Find the perimeter. Simplify the answer
    7·2 answers
  • A certain species of bird is in danger of becoming extinct. There were 1500 birds in 2000 and they are
    15·1 answer
  • I don't understand would this be a linear function,quadratic function,or exponential function
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!