SOLUTION: Can you pleae assist me with my childs homework. I have forgotten how to solve this type of problem. Thank you very much. The length of a rectangle is 1 cm longer than it width.

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Question 116988: Can you pleae assist me with my childs homework. I have forgotten how to solve this type of problem. Thank you very much.
The length of a rectangle is 1 cm longer than it width. If the diagonal of the rectangle is 5cm, what are the dimensions of the rectangle in centimeters?
Width=_______cm Length=________cm
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Let W=width, L=length

Since the length is 1 cm longer than it width, this means . So if the diagonal is 5 cm, we can find the lengths of the sides given this information

If we cut the rectangle in half along the diagonal, we'll basically have this triangle set up:

So we can use Pythagoreans Theorem to find the dimensions

Plug in

Square 5

Foil

Subtract 25 from both sides

Subtract 25 from both sides

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
or

or NoW solve for W in each case

So our possible answers are
or

However, since a negative width doesn't make sense, our only solution is

Now to find the length, simply add 1 to the width to get

so the width is 3 cm and the length is 4 cm

Check:

Start with the given equation

Plug in W=3 and L=4

Square each term

Add. Since the two sides of the equation are equal, this verifies our answer.