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wisammy
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Geometry strategy guide-page 106-problem 11--possible error?

by wisammy Tue Jul 22, 2014 11:20 pm

The triangle ABD is inscribed in a circle, such that AD is a diameter of the circle and angle BAD is 45(degrees). If the area of triangle ABD is 72 square units, how much larger is the area of the circle than the area of the triangle ABD?

I follow the problem completely until the last step.

If AD is the diameter, then it is a 45-45-90, and thus base and height are equal. Therefore (x^2)/2=72... x = 12.. therefore the hypotenuse (AD) is 12sqrt(2) and thus the diameter is 6sqrt(2)..

So, area of a circle is pi(r^2) --> pi(6sqrt(2)^2)

6 squared is 36.. but the book says 6 squared is 72.. I have a feeling I am missing something..

Could someone please help out.. this is the 3rd edition book.

Solution is on page 110.

Thanks.
yx33
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Re: Geometry strategy guide-page 106-problem 11--possible error?

by yx33 Wed Jul 23, 2014 11:39 am

You process is correct until the last step. The radius, not the diameter, is sqrt(72) or 6sqrt(2). Thus the area of the circle is pi[sqrt(72)]^2=72pi. The difference is 72pi-72
wisammy Wrote:So, area of a circle is pi(r^2) --> pi(6sqrt(2)^2)

6 squared is 36.. but the book says 6 squared is 72.. I have a feeling I am missing something..

Maybe you forgot to square the sqrt(2)?
wisammy
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Re: Geometry strategy guide-page 106-problem 11--possible error?

by wisammy Wed Jul 23, 2014 11:45 am

I meant to say radius.. but it doesn't change the math..

I simply don't see how they got 72 from 6^2..

it is really perplexing to me!
yx33
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Re: Geometry strategy guide-page 106-problem 11--possible error?

by yx33 Wed Jul 23, 2014 12:09 pm

What value is the 36 you are referring to?
wisammy
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Re: Geometry strategy guide-page 106-problem 11--possible error?

by wisammy Wed Jul 23, 2014 10:26 pm

if you have the book. On the solution page, they square 6 to get 72... and we both know that the square of 6 is 36.. I just don't get it.
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Re: Geometry strategy guide-page 106-problem 11--possible error?

by tommywallach Fri Jul 25, 2014 1:05 pm

Hey Wisammy,

When you square 6 * rt. 2, you have to square BOTH parts:

6^2 = 36

(rt. 2)^2 = 2

2 * 36 = 72

Make sense?

-t
wisammy
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Re: Geometry strategy guide-page 106-problem 11--possible error?

by wisammy Fri Jul 25, 2014 6:06 pm

Umm.. Almost.. Square both parts of what?

Thank you for your help.
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Re: Geometry strategy guide-page 106-problem 11--possible error?

by yx33 Sun Jul 27, 2014 12:19 am

You need to square both 6 and the √2 to get 72.

In your original post, you said:

"So, area of a circle is pi(r^2) --> pi(6sqrt(2)^2)"

The value or r here is actually 6√2 not just 6, so you need to square both numbers to get the final value, which becomes 72pi, instead of 36pi.
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Re: Geometry strategy guide-page 106-problem 11--possible error?

by tommywallach Wed Jul 30, 2014 12:44 am

Make sense, Wisammy?

-t