SOLUTION: On this problem, my instructor asks that we use the Pythagoreans Theorem. The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4 cm, what

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Question 68720: On this problem, my instructor asks that we use the Pythagoreans Theorem.
The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4 cm, what are the dimensions (the length and the width) of the
rectangle?
I have come up with L = 2.44 cm and W = 1.44 cm. Is this correct???
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
I DID NOT COME UP WITH THE SAME ANSWER AS YOU BUT WE ARE FAIRLY CLOSE. MAYBE YOU CAN CHECK BOTH OUR SOLUTIONS----PTAYLOR

In a right triangle, the Pythagorean Theorem statesc%5E2=a%5E2%2Bb%5E2%29 where c is the hypotenuse and a and b are the respective sides.
Let x= width of rectangle
Then x+1=length of rectangle
We are told that the diagonal or{or hypotenuse of the triangle) is 4 cm. So or equation to solve is:
x%5E2%2B%28x%2B1%29%5E2=%284%5E2%29 clear parens
x%5E2%2Bx%5E2%2B2x%2B1=16 subtract 16 from both sides
2x%5E2%2B2x-15=0 quadratic in standard form
Using the quadratic formula: x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-2+%2B-+sqrt%28+4%2B120+%29%29%2F%284%29+
x+=+%28-2+%2B-+11.135%29%2F%284%29+

x+=+%28%2B9.135%29%2F%284%29+
x+=2.2837+cm -----------------------------width
x%2B1=2.2837%2B1=3.2837------------------------length
I think that we can discount the negative value for x

Hope this helps----ptaylor