The length of a room is 4 m longer it's width.find the length of the room if it's area is 32 m2.
The length of the room is 4 meters longer than its width, so the length (l) can be expressed as
w+4 meters.
Area of rectangle = L X W
Substitute the expressions for length and width:
32 = (4+w) * w
solve this quadratic equation for W:
32 = 4W + W2
w2+4w−32=0
factor the quadratic equation
(w+8)(w-4) =0
This equation has two solutions
W+8 = 0
w-4 = 0
first solution
w+8 = 0
w = -8 (width cannot be negative, ignore these)
second
w-4 = 0
w = 4 (width is positive, take this)
since width cannot be negative, we discard the first answer hence
w=4
length of the room L = L + w
L = 4 + 4 = 8 m
Note : length of the room is 4+x and x is equal to 4.
4+4=8m
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