# SOLUTION: The width of a room is 3 feet shorter than its length. The perimeter of the room is 62 ft. What is the length and width?

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Question 84663: The width of a room is 3 feet shorter than its length. The perimeter of the room is 62 ft. What is the length and width?

Found 2 solutions by liz_gcmama, abbeysin:
You can put this solution on YOUR website!
Let's give the room a length of n.
The width of the room is z.
The perimeter of the room would be n+z+n+z or 2n+2z.
We know that the width is 3 feet shorter than the length so we know that z=n-3.
If we substitute that into the above perimeter formula we find that the perimeter equals 2n+2(n-3). We know that the perimeter equals 62ft so we can say that
2n+2(n-3)=62
subtract 62 from each side
2n+2(n-3)-62=0
expand the brackets
2n+2n-6-62=0
simplify
4n-68=0
divide both sides by 4
4n/4-68/4=0/4
n-17=0
n=17
Now n is the length. So we know the length is 17.
The width is n-3, so the width is 17-3 = 14.
Let's check that our answer is correct.
17+17+14+14=62.
Therefore length=17, width=14.

You can put this solution on YOUR website!
Let the width be X
and then let the Length be Y
so if length is 3 less than width
then Y = X - 3
perimeter = 62
so as per the formula-
perimeter = 2(w X h) = 2(X X Y)
so 62 = 2(X(X - 3))
62 = 2(x^2 - 3x)
62 = 2x^2 - 6x
2x^2 - 6x - 62=0
So after this we have
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=532 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4.2662812973354, -7.2662812973354. Here's your graph:

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