Algebra(or maybe geometry...)problem?

Question

if anyone can explain this problem to me or how to do it...i would be eternally grateful...
http://i44.photobucket.com/albums/f49/jackie9725/untitled.jpg

Answer 1

You could say that the base of the smaller triangle is half the size of its hypotenuse and it is a ration of triangles. You could look at it as a ratio:
5/10=10/x
solving for x you get 20

another way of doing it is to dig into algebra:
S^2=10^2+X^2
X^2=S^2-100

Now substitute:
5^2+Y^2=10^2 where Y is the vertical part of the smaller triangle
25+Y^2=100
Y^2=75
Y=sq. root 75

The hypotenuse of the larger triangle is labeled S and the base of it is 10 and the other side can be labeled X.
S/X=10/Y(this is comparing the sides of the two triangles)
cross multiply and get SY=10X
From above, we know that Y=_/75(that means sq. root of 75)
Substitute this in the SY=10X and get S_/75=10X
To get rid of the sq root sign, just square everything.
You get S^2(75)=100X^2
Also, from above, we showed that X^2=S^2-100
So, substitute and get:
75S^2=100(S^2-100)
75S^2=100S^s-10,000
-25S^2=-10,000
Change both sides to a+
25S^2=10,000
S^2=10,000/25
S^2=400
S=20

Answer 2

s= 20
first use 30 60 90 triangle rule to get that the missing side from the smallest triangle is 5rt3
then the medium triangle is also a 30 60 90 triangle, so the longer leg is shorter leg (5rt3) times rt3 which = 15. Add that to the 5 that is already there and you get 20.....

Answer 3

make use pythagorean theorum for a right triangle.
A^2 + B^2 =C^2
Base^2 + Short leg^2 = Hypotenuse ^2

call inside segment z
call lower left segment x
call upper left segment y

x^2 = 10^2 - 5^2 = 75

Y^2 + 10^2 =s^2
(s-5)^2 + 75 = Y^2

substitute and solve for s
(s-5)^2 + 75 +100 =s^2
S^2 -10S +25 +175 =s^2
subtract s^2 from both sides
200 = 10S
s = 20

Enjoy!

Answer 4

it is twenty, the little triangle is half an equilaateral triangle,means you can use the propertis of sin, cosine or tanget, the best to use is tangent, opposite over adjacent, the lower right angle is 60 degrees an the upper one is 30, the choice is 60, the equation should look like this
tan60=x/5
x being the little leg of the right triangle
by solvng this equation you get 8.66
as you might notice the bigger triangle is also part of an equilateral
by knowing this use the same equation as above which should look like this
tan60=(y/8.66)+5
by doing this it is about twenty, hope this helps

Answer 5

The hypotenuse in a right triangle is equal to one and one half times the sum of both sides.

Answer 6

i think i got it, i don't know how to explain it though. s=20
the triangles are are similar, the bigger one is twice the size of the smaller, and since S is similar to the side 10 on the small it is twice of 10 which is 20. if u don't get it email me and ill try explaining it better.

Answer 7

it's c.15

Answer 8

s=15, I didn't know how to do part of the equation but I did what part I knew and estimated it from there.

Answer 9

One shall not depend on others...
~Sahib~