A Geometric Mean Prob
- Thread starter mcbeth39
- Start date
mcbeth39 said:
On what do you base your statement that "the answer is 4."?
You have an isosceles triangle (the large triangle) with equal sides of 6, and a base of 8. You have an altitude drawn to the base of the triangle. It is easy to prove that the two smaller triangles formed are congruent, and that the altitude bisects the base of the isosceles triangle. So...each of the small triangles has a leg of x, another leg of 4, and a hypotenuse of 6.
Use the Pythagorean Theorem:
x[sup:1y0rkyn2]2[/sup:1y0rkyn2] + 4[sup:1y0rkyn2]2[/sup:1y0rkyn2] = 6[sup:1y0rkyn2]2[/sup:1y0rkyn2]
x[sup:1y0rkyn2]2[/sup:1y0rkyn2] + 16 = 36
Can you finish it now?
I did have x squared+ 16= 36 above
and if you subtract 16 from 36 you get 20. In order to get rid of x squared you square root them.
x= 4.47
I get the answer of 4 because a friend of mine said she got that in class. Instead of just writing it down I wanted to know how she got it. But then the bell rang.
It is a multiple choice answer.
The choices are 3, 4, 4 times the square root of 3, and 2 times the square root of 5
and if you subtract 16 from 36 you get 20. In order to get rid of x squared you square root them.
x= 4.47
I get the answer of 4 because a friend of mine said she got that in class. Instead of just writing it down I wanted to know how she got it. But then the bell rang.
It is a multiple choice answer.The choices are 3, 4, 4 times the square root of 3, and 2 times the square root of 5
mcbeth39 said:I did have x squared+ 16= 36 above
and if you subtract 16 from 36 you get 20. In order to get rid of x squared you square root them.
x= 4.47
I get the answer of 4 because a friend of mine said she got that in class. Instead of just writing it down I wanted to know how she got it. But then the bell rang.
The choices are 3, 4, 4 times the square root of 3, and 2 times the square root of 5
Obviously you believe your friend is an authority....
I get the answer of 4 because a friend of mine said she got that in class.
Working with
x[sup:k7syn00c]2[/sup:k7syn00c] + 16 = 36
we can subtract 16 from both sides of the equation:
x[sup:k7syn00c]2[/sup:k7syn00c] + 16 - 16 = 36 - 16
x[sup:k7syn00c]2[/sup:k7syn00c] = 20
Take the square root of both sides of the equation:
sqrt[x[sup:k7syn00c]2[/sup:k7syn00c]] = sqrt(20)
x = sqrt(20)
Now....I'm pretty sure you have covered simplifying radicals. How would you simplify sqrt(20)?
sqrt(20) does simplify to one of your multiple choice answers.
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You need a little more than a hint.
"4 squared + 6 squared = x squared"
You need also a little care and caution. Before applying the Pythagorean Theorem, make sure you know which two sides are legs and which one isn't.
"the answer of 4 because a friend of mine said she got that in class"
You need a little rigor. Lacking an isosceles triangle (is was when you started, but you cut it in half), why would the answer be 4? Before you buy someone else's answer, take the time to learn WHY things are as they are.
"4 squared + 6 squared = x squared"
You need also a little care and caution. Before applying the Pythagorean Theorem, make sure you know which two sides are legs and which one isn't.
"the answer of 4 because a friend of mine said she got that in class"
You need a little rigor. Lacking an isosceles triangle (is was when you started, but you cut it in half), why would the answer be 4? Before you buy someone else's answer, take the time to learn WHY things are as they are.