SOLUTION: section 9.6 # 46 Geometry. The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 5 cm, what are the dimensions (the length and width) of

Question 73993: section 9.6 # 46

Geometry. The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 5 cm, what are the dimensions (the length and width) of the rectangle?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let L=length, w=width.
The length and width can be represented as

The diagonal of the rectangle is the hypotenuse of the triangle with legs of L and w. So the length and width can be found by Pythagoreans theorem.
Plug in w+1 into L
foil the (w+1)^2 term
Combine like terms and get everything to one side

Plug this into the quadratic equation to solve for w

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=196 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3, -4. Here's your graph:

This means the width is 3 (the negative width is ignored since it's not practical). So the length is

So the dimensions are: Width=3,Length=4

Check:

Works

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