Question 600376: A kitchen floor is 3 feet longer thann it is wide. The area of the floor is 180 square feet. Find the demensions of the kitchen.
Found 2 solutions by jim_thompson5910, mamiya:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! A = LW
A = (W+3)W
A = W(W+3)
180 = W(W+3)
180 = W^2 + 3W
0 = W^2 + 3W - 180
W^2 + 3W - 180 = 0
Now use the quadratic formula to solve for W
W = (-b+-sqrt(b^2-4ac))/(2a)
W = (-(3)+-sqrt((3)^2-4(1)(-180)))/(2(1))
W = (-3+-sqrt(9-(-720)))/(2)
W = (-3+-sqrt(729))/2
W = (-3+sqrt(729))/2 or W = (-3-sqrt(729))/2
W = (-3+27)/2 or W = (-3-27)/2
W = 24/2 or W = -30/2
W = 12 or W = -15
Toss out the negative result to get the only answer of W = 12
So the width is 12.
The length is 3 more than the width. So the length is L = W+3 = 12+3 = 15
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Answer:
The length is 15 feet and the width is 12 feet
Answer by mamiya(56) (Show Source):
You can put this solution on YOUR website! let l be the length of the kitchen and, w its width.
The kitchen is 3 feet longer than its width, means l = w +3
the area of the floor is 180, means l*w= 180
so we have to solve the following system
l-w = 3
l*w=180
At this point , there are many ways to solve the problem.
first , let's do this with the method i consider the easiest one but sometimes the longest one
we have to find all pairs of numbers whose product is 180 and look for the one whose difference is 3
we have: ( 1, 180) (2, 90) (3, 60) (4, 45) ( 5, 36), (6, 30) ( 9, 20) ( 10, 18) (12, 15)....
I stopped at ( 12, 15) because 15-12= 3 so the answers are 12ft and 15ft ( we can keep going with the list but that would be a complete waste of time)
Another way
you pick an equation from the system, write one letter in term of the other one and then plug that in the other equation, and solve the final equation we get.
l= w+ 3 --> l*w = (w+3)*w = 180
--> w^2 + 3w -180 = 0
now we use the quadratic formula to solve for w
w = (-3 + sqrt(3^2-4(-180)))\2
= (-3 + sqrt(9+720))\2
= (-3 + 27)/2
= 24\2
= 12
l = w+3 = 12 + 3 + 15
(Notice that i only use the one where the plus inside because the other one with the minus inside, will give us a negative numbers, and we are talking about dimensions so positive numbers. )
So the dimensions of that kitchen is 12ft and 15ft
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