SOLUTION: a rectangles length is three times its width. its diagonal is 10 inches. how many inches is it's width?

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Question 552088: a rectangles length is three times its width. its diagonal is 10 inches. how many inches is it's width?
Answer by neatmath(302) About Me  (Show Source):
You can put this solution on YOUR website!

In this problem, we have 2 unknowns, and 1 known.

We don't know the length or the width exactly, though we do know how they are related.

We do know the diagonal is 10 inches.

We can solve this by drawing a sketch and using the Pythagorean Theorem!!!

Let L be the length. Let W be the width.

L=3W given

%283W%29%5E2%2BW%5E2=10%5E2 length squared plus width squared equals diagonal squared

9W%5E2%2BW%5E2=100

10W%5E2=100

W%5E2=10

W=sqrt%2810%29 or W=-sqrt%2810%29

Since lengths MUST be positive, we can discard the second answer of -10.

So it looks like our width is sqrt%2810%29 inches.

Then our length is simply 3%2Asqrt%2810%29 inches.

I hope this helps! :)

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