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Acerbated Offline
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Quick math question :] - February 12th 2009, 03:32 AM

I'm in math20 this semester, we're doing some stuff with radicals. I can't get the answer to this one question, and neither can the other 7 people age ranged 15-21 I've asked. Since TH is full of intelligent people, I figured somebody here must know how to do it and could explain it to me :]

"Find the perimeter of a rectangle if it's width is 4cm and the length of it's diagonal is 6 cm. Express your answer as a radical in simplest form"

Diagram included with a rectangle, the short side labeled 4cm and the diagonal as 6cm, as described.

The answer is 8 + 4√5, I'm just getting 20. One person I asked tried two different ways, got 20, the rest just have no idea on how to do it :[

Halp?


Every time I try to give up, a little voice called hope says "one more try"
   
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Re: Quick math question :] - February 12th 2009, 09:23 AM

well i got the answer you want. As u have been given the side of a rectangle and its diagonal, you can use pythagoras (sp) to work out the other side

6^2 - 4^2 = 20 so the side is √20. which can be written as 2√5.

then you just work out the perimeter so:

4+4+2√5+2√5 = 8 + 4√5

Last edited by ~sal~; February 12th 2009 at 09:24 AM. Reason: typo
   
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Re: Quick math question :] - February 12th 2009, 09:36 AM

Quote:
Originally Posted by Acerbated View Post
I'm in math20 this semester, we're doing some stuff with radicals. I can't get the answer to this one question, and neither can the other 7 people age ranged 15-21 I've asked. Since TH is full of intelligent people, I figured somebody here must know how to do it and could explain it to me :]

"Find the perimeter of a rectangle if it's width is 4cm and the length of it's diagonal is 6 cm. Express your answer as a radical in simplest form"

Diagram included with a rectangle, the short side labeled 4cm and the diagonal as 6cm, as described.

The answer is 8 + 4√5, I'm just getting 20. One person I asked tried two different ways, got 20, the rest just have no idea on how to do it :[

Halp?

Use Pythagoras' Theorem to find the length (a) of your rectangle such that:

6^2 = a^2 + 4^2

a^2 = 20 and a is therefore √20. (or -√20 but we may ignore it since a scalar length must be greater than 0).

Using the rule √(ab) = √a * √b and knowing that 20 = 4*5 we can say that √20 = √4 * √5 = 2√5.

To find the perimeter we do 2a + 2b = 2(a+b) where b is the width (ie 4cm).

P = 2(2√5 + 4) = 4√5 + 8 = 8+4√5
   
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