# SOLUTION: The length of a rectangle is 5 inches longer than the width. The area of the rectangle is 50 inches squared. Find the length and the width of the rectangle.

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 Question 572708: The length of a rectangle is 5 inches longer than the width. The area of the rectangle is 50 inches squared. Find the length and the width of the rectangle.Answer by mathsmiles(68)   (Show Source): You can put this solution on YOUR website!First thing we want to do is write down what we know: Area of a rectangle: A = L x W L = 5 + W (length is 5 inches longer than the width) A = 50 (Area is 50 inches squared) Putting this all together: L x W = 50 Substituting for L with the above equation: (5+W) x W = 50 Multiplying out the paren 5W + W^2 = 50 Subtract 50 from both sides and rearrange the terms a little: W^2 + 5W - 50 = 0 Now solve: (W _ _) (W _ _) = 0 (we need to figure out the operand and the term for each) The negative whole number indicates these have different signs (W - _) (W + _) = 0 We need to find two factors of 50 whose difference (subtract them) gives 5. 50 = 25 x 2 Nope 50 = 5 x 10 Yup! Since the 5W term is positive, we need to put the 10 in the positive factor and 5 in the negative factor so ... (W - 5)(W + 10) = 0 W -5 = 0 W = 5 W + 10 = 0 W = -10 Since we're talking about the area of a rectangle, we have to assume it has positive sides or we've just entered another dimension. :-) So, W = 5 inches L = 5 + 5 (5 inches longer than the width) L = 10 inches Checking: A = L x W A = 5 x 10 50 = 50 Correct!