Solving Quadratics Word Problem

Question

The length of a rectangle is 10 inches greater than the width. If the area is 375 square inches, (A) write an equation to determine the width. (B) Solve for the length and width of the rectangle.

Please explain also, not just the answer

-Ellie E

Answer 1

Let l= length and w= width. Then area = lw = 375 in² .The problem states that the length is 10 in greater than the width which means l= w + 10 so use this in the area formula to get 375 = w(w + 10) = w² +10w. So the equation becomes w² +10 w +25 = 375 +25 by completing the square. So (w+ 5)²= 400. Taking the square root of both sides gives w+ 5= ± 20. Take the positive root and w+5 = 20 or w= 15 and l= w+10= 25.