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.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> 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.      Log On


   

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) About Me  (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 L=W%2B1. 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

W%5E2%2BL%5E2=5%5E2


W%5E2%2B%28W%2B1%29%5E2=5%5E2 Plug in L=W%2B1



W%5E2%2B%28W%2B1%29%5E2=25 Square 5



W%5E2%2BW%5E2%2B2W%2B1=25 Foil


W%5E2%2BW%5E2%2B2W%2B1-25=0 Subtract 25 from both sides


2W%5E2%2B2W-24=0 Subtract 25 from both sides




2%28W%2B4%29%28W-3%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
W%2B4=0 or W-3=0

W=-4 or W=3 NoW solve for W in each case


So our possible answers are
W=-4 or W=3

However, since a negative width doesn't make sense, our only solution is W=3


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

3%2B1=4

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


Check:

W%5E2%2BL%5E2=5%5E2 Start with the given equation



3%5E2%2B4%5E2=5%5E2 Plug in W=3 and L=4


9%2B16=25 Square each term


25=25 Add. Since the two sides of the equation are equal, this verifies our answer.