SOLUTION: Hello, my question is this: The length of a rectangle is 1cm longer than its width. If the diagonal of the rectangle is 4cm, what are the dimensions (the length and width) of the r

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Question 91120: Hello, my question is this: The length of a rectangle is 1cm longer than its width. If the diagonal of the rectangle is 4cm, what are the dimensions (the length and width) of the rectangle?
I started with a sketch of the problem and came up with the equation
x^2+(x+1)^2=4^2
x^2+x^2+2x+1=16
2x^2+2x-15=0
Now I don't know where to go from here Help me please!
Found 2 solutions by vertciel, jim_thompson5910:
Answer by vertciel(183) About Me  (Show Source):
You can put this solution on YOUR website!
I am not sure if I was the person who helped you with this problem earlier; this problem seems familiar.
2x^2 + 2x - 15 = 0
You can't factor to solve for the x roots so you'll have the use the quadratic formula.
x+=+%28-2+%2B-+sqrt%28+%282%29%5E2-4%2A%282%29%2A%28-15%29+%29%29%2F%282%2A2%29+
There you are.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's use the quadratic formula to solve for x:


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve 2%2Ax%5E2%2B2%2Ax-15=0 ( notice a=2, b=2, and c=-15)

x+=+%28-2+%2B-+sqrt%28+%282%29%5E2-4%2A2%2A-15+%29%29%2F%282%2A2%29 Plug in a=2, b=2, and c=-15



x+=+%28-2+%2B-+sqrt%28+4-4%2A2%2A-15+%29%29%2F%282%2A2%29 Square 2 to get 4



x+=+%28-2+%2B-+sqrt%28+4%2B120+%29%29%2F%282%2A2%29 Multiply -4%2A-15%2A2 to get 120



x+=+%28-2+%2B-+sqrt%28+124+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-2+%2B-+2%2Asqrt%2831%29%29%2F%282%2A2%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-2+%2B-+2%2Asqrt%2831%29%29%2F4 Multiply 2 and 2 to get 4

So now the expression breaks down into two parts

x+=+%28-2+%2B+2%2Asqrt%2831%29%29%2F4 or x+=+%28-2+-+2%2Asqrt%2831%29%29%2F4


Now break up the fraction


x=-2%2F4%2B2%2Asqrt%2831%29%2F4 or x=-2%2F4-2%2Asqrt%2831%29%2F4


Simplify


x=-1+%2F+2%2Bsqrt%2831%29%2F2 or x=-1+%2F+2-sqrt%2831%29%2F2


So these expressions approximate to

x=2.28388218141501 or x=-3.28388218141501


So our solutions are:
x=2.28388218141501 or x=-3.28388218141501

However, since a negative length doesn't make sense, our only solution is x=2.28388218141501

So the width is about 2.284 cm and the length is 3.284 cm