SOLUTION: Geometry. 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?

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Question 75835This question is from textbook Beginning Algebra
: Geometry. 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 am needing some help with this, can you please help me? Thanks This question is from textbook Beginning Algebra

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=width
Then x+1=length
When we draw the diagonal of a rectangle we, in effect, draw the hypotenuse of two identical right triangles whose sides are the length and width of the rectangle. We can therefore apply the Pythagorean Theorem:
a%5E2%2Bb%5E2=c%5E2 or
x%5E2%2B%28x%2B1%29%5E2=4%5E2 get rid of parens
x%5E2%2Bx%5E2%2B2x%2B1=16 subtract 16 from both sides
2x%5E2%2B2x%2B1-16=16-16
2x%5E2%2B2x-15=0 quadratic in standard form
We will solve 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+2%5E2-4%2A2%2A%28-15%29+%29%29%2F%282%2A2%29+
x+=+%28-2+%2B-+sqrt%28+4%2B120%29%29%2F%284%29+
x+=+%28-2+%2B-+%2811.136%29%29%2F%284%29+
x+=+%28-2+%2B%2811.136%29%29%2F%284%29+
x+=+%289.136%29%2F%284%29+

x=2.284 cm------------------------width
x%2B1=2.284%2B1=3.384cm-----------------------length
We will ignore the negative value for x ( lengths and widths are positive)

CK
%282.284%29%5E2%2B%283.284%29%5E2=4%5E2
5.217%2B10.784=16
16=16

Hope this helps------ptaylor