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

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 problem
Found 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(4671) (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.
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