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
quester [9]
3 years ago
14

A rectangular parking lot has an area of 15,000 feet squared, the length is 20 feet more than the width. Find the dimensions

Mathematics
1 answer:
faust18 [17]3 years ago
3 0

Dimension of rectangular parking lot is width = 112.882 feet and length = 132.882 feet

<h3><u>Solution:</u></h3>

Given that  

Area of rectangular parking lot = 15000 square feet

Length is 20 feet more than the width.

Need to find the dimensions of rectangular parking lot.

Let assume width of the rectangular parking lot in feet be represented by variable "x"

As Length is 20 feet more than the width,

so length of rectangular parking plot = 20 + width of the rectangular parking plot

=> length of rectangular parking plot = 20 + x = x + 20

<em><u>The area of rectangle is given as:</u></em>

\text {Area of rectangle }=length \times width

Area of rectangular parking lot = length of rectangular parking plot \times width of the rectangular parking

\begin{array}{l}{=(x+20) \times (x)} \\\\ {\Rightarrow \text { Area of rectangular parking lot }=x^{2}+20 x}\end{array}

But it is given that Area of rectangular parking lot = 15000 square feet

\begin{array}{l}{=>x^{2}+20 x=15000} \\\\ {=>x^{2}+20 x-15000=0}\end{array}

Solving the above quadratic equation using quadratic formula

<em><u>General form of quadratic equation is  </u></em>

{ax^{2}+\mathrm{b} x+\mathrm{c}=0

And quadratic formula for getting roots of quadratic equation is

x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}

In our case b = 20, a = 1 and c = -15000

Calculating roots of the equation we get

\begin{array}{l}{x=\frac{-(20) \pm \sqrt{(20)^{2}-4(1)(-15000)}}{2 \times 1}} \\\\ {x=\frac{-(20) \pm \sqrt{400+60000}}{2 \times 1}} \\\\ {x=\frac{-(20) \pm \sqrt{60400}}{2}} \\\\ {x=\frac{-(20) \pm 245.764}{2 \times 1}}\end{array}

\begin{array}{l}{=>x=\frac{-(20)+245.764}{2 \times 1} \text { or } x=\frac{-(20)-245.764}{2 \times 1}} \\\\ {=>x=\frac{225.764}{2} \text { or } x=\frac{-265.764}{2}} \\\\ {=>x=112.882 \text { or } x=-132.882}\end{array}

As variable x represents width of the rectangular parking lot, it cannot be negative.

=> Width of the rectangular parking lot "x" = 112.882 feet  

=> Length of the rectangular parking lot = x + 20 = 112.882 + 20 = 132.882

Hence can conclude that dimension of rectangular parking lot is width = 112.882 feet and length = 132.882 feet.

You might be interested in
Which of the following has a positive value? sec (2pi/3) tan (2pi/3) cos (2pi/3) csc (2pi/3)
Darya [45]

Answer:  D) csc (2π/3)

<u>Step-by-step explanation:</u>

2π/3 is in Quadrant II

Quadrant II has a negative x-value and a positive y-value.

x-values are: cos & sec

y-values are: sin & csc

tan = y/x so will be negative in Quadrant II

A) sec = -

B) tan = -

C) cos = -

D) csc = +     this works!

7 0
3 years ago
Answer only one question​ No 1 only
Dafna1 [17]
The answer is -10,368 ;)
7 0
3 years ago
Solve equation<br>8-3(p-4)=2p
LenKa [72]

Answer:

ok the answer is: p=-4

Step-by-step explanation:

First you distribute 3 times p-4 and get  8-3p+12=2p then you add 12 plus 8 and get 20 then you have 20-3p=2p you have to add 3p on both sides and you get 20= -5p you divide and get p= -4

6 0
3 years ago
Steven made snack mix he used 1/4 cup of raisins and 2/4 cups of nuts to make 1 serving how many cups to make 5 servings
suter [353]
1 and 1/4 cup of raisins and 2 and 1/2 cups of nuts for a total of 3 and 3/4 cups.
7 0
3 years ago
How many solutions does this linear system of equations have?
Irina18 [472]
It has infinite solutions
4 0
3 years ago
Read 2 more answers
Other questions:
  • Best Cam'ron 3 miles and 25.8 minutes how long does it take her to run 1 mile
    12·1 answer
  • A chef at a restaurant uses 22 pounds of butter each day. About how many grams of butter does theA chef at a restaurant uses 22
    11·1 answer
  • Evaluate 8r<br> rs when r<br> 6 and s = 5.
    7·2 answers
  • Write an equation for the translation of y=|x| up to 0.75 units.
    6·1 answer
  • REALLY NEED HELP ~20 points
    6·2 answers
  • Plsss help Get brainiest if right!!
    13·2 answers
  • Is it positive negative or none?
    11·1 answer
  • (8 x 10-^3) - (2 x 10-^5)
    9·1 answer
  • The coefficient of y in 2x – 3y is ------------------- (3, -3, 2)
    6·1 answer
  • Change 3/8 to percent
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!