the length of the floor is 12 m longer than its width and the area is less than or equal to 45 square meters
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the length of the floor is 12 m longer than its width and the area is less than or equal to 45 square meters
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Let W = Width. Units are meters (m)
Let L = Length = W + 4
What do we know about the area of a rectangle.
A = L x W and A = 45 m^2. Therefore just substitute and solve.
45 = (W + 4)W
45 = W^2 + 4 W or
W^2 + 4 W - 45 = 0 Now factor or you us the quadratic formula.
(W + 9)(W - 5) = 0 so W + 9 = 0 or W - 5 = 0 =>
W = -9 or W = 5 the equation has 2 solutions but dimensions are only positive so we use W = 5
Therefore, W = 5m and L = W + 4 = 9m
Check: 9 x 5 = 45 correct.
Answer: W = 5m and L = 9m