SOLUTION: Would someone please show the solution to this word problem step by step. Thank you. The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4

Question 87998: Would someone please show the solution to this word problem step by step. Thank you.
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?
Answer by tutor_paul(519) (Show Source): You can put this solution on YOUR website!
The diagonal of the rectangle forms the hypoteneuse of a right triangle with the legs of said triangle being the length and the width of the rectangle. Wow, that
was a mouthful. Anyways, they give you that l=w+1. So you can use the pythagorean theorem to write an equation for w:

Square the binomial and simplify the right hand side:

Put the quadratic in standard form and combine like terms:

Use the quadratic formula:

Simplify:

You need to have a positive value for the width, so throw away the negative result:

Simplify a little more:

You can plug this into your calculator if you need a numerical value.
from the given information, l is just 1+w.
Good Luck,
tutor_paul@yahoo.com

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