Finding triangle's area

[The Preacher]

The lengths of the sides of a right triangle are a and b, and the hypotenuse is c. Find the area of the triangle.

I'd be able to find the other side, then the area... but it involves a square root thing. My mind inexplicably locks up when I see one. I can't get past it.

Here's what I've got so far:

Use the Pythagorean Theorem to find b.

6 x 6 = 36 --- \(\displaystyle c^2\)=36

2 x 2 = 4 --- \(\displaystyle a^2\)=4

36-4=32 --- \(\displaystyle c^2-a^2=32\)

Now I just have to find out what 32 is the square of, but I can't. Also, from looking at the problem, the answer is going to be in radical form, so I probably won't know what to do afterward either.

Sorry to be so useless about math... at least I can use TeXaide. Thanks guys.

-The Preacher

 

[TchrWill]

The lengths of the sides of a right triangle are a and b, and the hypotenuse is c. Find the area of the triangle.



I'd be able to find the other side, the the area... but it involves a square root thing. My mind inexplicably locks up when I see one. I can't get past it.

Here's what I've got so far:

Use the Pythagorean Theorem to find b.

6 x 6 = 36 --- =36

2 x 2 = 4 --- =4

36-4=32 ---

Now I just have to find out what 32 is the square of, but I can't. Also, from looking at the problem, the answer is going to be in radical form, so I probably won't know what to do afterward either.

You were on the right track as b = sqrt(32).

Therefore, the area is A = 2sqrt(32)/2 = sqrt(32).= 2sqrt(8).

 

[The Preacher]

Therefore, the area is A = 2sqrt(32)/2 = sqrt(32).= 2sqrt(8).

So... 2 times the square root of 32 divided by two equals the square root of 32. How do you get from sqrt(32) to 2sqrt(8)? What are you doing to it to make it 2sqrt(8)?

 

[stapel]

Try factoring 32.

Eliz.

 

[The Preacher]

Try factoring 32.

Eliz.

Thanks. When I factor 32, what am I looking for in the numbers? Or, to say it differently, how do I pick the right factors?

 

[stapel]

...how do I pick the right factors?

Just factor it completely. Then whatever you've got two copies of, take outside the root.

Note: The expression "sqrt[32]" simplifies more than just "2sqrt[8]".

Eliz.

 

[The Preacher]

...how do I pick the right factors?

Just factor it completely. Then whatever you've got two copies of, take outside the root.

Note: The expression "sqrt[32]" simplifies more than just "2sqrt[8]".

Eliz.

Alright, thanks for your help. I took your advice, and found the answer to be 4sqrt(2). Thanks again, stapel.

 

[TchrWill]

So... 2 times the square root of 32 divided by two equals the square root of 32. How do you get from sqrt(32) to 2sqrt(8)? What are you doing to it to make it 2sqrt(8)?

sqrt(32) = sqrt(4x8)

Extracting the sqrt(4) = 2, we get 2sqrt(8)

 

[The Preacher]

So... 2 times the square root of 32 divided by two equals the square root of 32. How do you get from sqrt(32) to 2sqrt(8)? What are you doing to it to make it 2sqrt(8)?

sqrt(32) = sqrt(4x8)

Extracting the sqrt(4) = 2, we get 2sqrt(8)

Thanks, TchrWill, that makes it even simpler. I'll try to remember it.

God bless,
-The Preacher

 

[Denis]

Just so you don't get confused, Preacher:
sqrt(32) = sqrt(4 * 8) = 2sqrt(8) is correct, BUT really should be:
sqrt(32) = sqrt(16 * 2) = 4sqrt(2) : as YOU have it...congrats