SOLUTION: I have tried figuring this one out, but no luck. Can you please help me? A rectangular parking lot has a length that is 3 yards greater than the width. The area of the parking l

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I have tried figuring this one out, but no luck. Can you please help me? A rectangular parking lot has a length that is 3 yards greater than the width. The area of the parking l      Log On


   

Question 122304: I have tried figuring this one out, but no luck. Can you please help me?
A rectangular parking lot has a length that is 3 yards greater than the width. The area of the parking lot is 180 square yards. Find the length and the width.
This is how I set up the equation: x(x+3)=180 but it doesn't work out.
Found 2 solutions by Fombitz, jim_thompson5910:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You set it up right.
Let see where it goes.
x%28x%2B3%29=180
x%5E2%2B3x=180
x%5E2%2B3x-180=0
You can factor this quadratic equation.
%28x%2B15%29%28x-12%29=0
x=-15 and x=12 solve the equation.
Since we're interested in a measurement, the negative value doesn't make sense.
x=12.
Check your answer.
x%28x%2B3%29=180
12%2812%2B3%29=180
12%2815%29=180
180=180
True statement.
Your answer is correct.
Where'd you get stuck?

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You have the correct equation set up

x%28x%2B3%29=180 Start with the given equation



x%5E2%2B3x=180 Distribute



x%5E2%2B3x-180=0 Subtract 180 from both sides


%28x%2B15%29%28x-12%29=0 Factor the left side. Note: if you need help with factoring , check out this solver.



Set each factor equal to zero


x%2B15=0 or x-12=0


Now solve for x in each case

x=-15 or x=12



Since a negative length/width doesn't make any sense, our only solution is


x=12



So this means that the width is 12 yards. Now to find the length, simply add 3 yards to 12 to get 12%2B3=15. So the length is 15 yards



Check:

Simply multiply the width 12 and the length 15 to get


12%2A15=180

which is the area.

So this verifies our answer.