# SOLUTION: One side of a rectangle is 7 cm longer than the other side. The diagonal is 8 cm longer than the shortest side of the rectangle. Find the dimensions of the rectangle. I am stuck an

Algebra ->  Algebra  -> Rectangles -> SOLUTION: One side of a rectangle is 7 cm longer than the other side. The diagonal is 8 cm longer than the shortest side of the rectangle. Find the dimensions of the rectangle. I am stuck an      Log On

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 Question 4129: One side of a rectangle is 7 cm longer than the other side. The diagonal is 8 cm longer than the shortest side of the rectangle. Find the dimensions of the rectangle. I am stuck and do not know how to solve this problemFound 2 solutions by ivankst, rapaljer:Answer by ivankst(3)   (Show Source): You can put this solution on YOUR website!Let a and b be sides of a rectangle, and d a diagonal. Let . We have following equations: By using Pythagorean theorem you can calculate that So our system of equations becomes: If we put in second equation, we get: or b cannot be a negative number, so b=5. First eqaution gives us a: So, sides of a rectangle are: (5,12). Answer by rapaljer(4667)   (Show Source): You can put this solution on YOUR website!Let x = first side of the rectangle (width) x+7 = second side of the rectangle (length) x+8 = diagonal of the rectangle (hypotenuse of the right triangle) This is a quadratic equation, so set it equal to zero! Factor the left side: x = 5 or x = -3 Since x is a side of a triangle, it cannot be negative. Therefore reject the x=-3. If x = 5, then x + 7 = 12, and x + 8 = 13. The rectangle is 5 by 12 and the diagonal is 13.