Inside the large triangle is a small triangle - what’s the missing side of the small triangle?

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[@stevendebettencourt7651]

Ah, similar triangles. Always a fun thing.
I’m not sure what theorem it is, but basically, if two triangles have the same angle measures, their sides will be proportional. For example, a 3-4-5 right triangle has the same angles as a 6-8-10 right triangle. Thus, if we compare the shortest sides to the longest sides:
3/6 = 5/10
Now, do the two triangles here have all the same angles? I say they do. Obviously, they have the same top angle, since they are top of one another. And both have a right angle. Because all triangles in flat space must have their angles add to 180 degrees (or pi radians), and since these triangles share two angle measures, the third must also be the same. So the sides will be proportional.
So, we need to find x, which is proportional to 10, but in what proportion? We have given that the measures of the other legs, so we can continue as follows:
x/10 = 6/(6+6) = 6/12
We can now cross multiply:
=> 12*x = 10*6
=> 12x = 60
=> x = 60/12
=> x = 5
So in this case, x = 5. We could also find the lengths of the two hypotenuses as well, but I’ll leave that as your homework. Here’s a hint: The longer one should be twice as long as the shorter one. But you already knew that.

[@PracticingLiberty]

5 baby 5!

[@russelllomando8460]

got 5 in 1 second 6:12 is to X:10 1/2 of 10 = 5 thanks for the fun

[@p38arover22]

It’s obviously 5. The drawing isn’t accurate.

[@tomtke7351]

X:6 = 10:12
or
X/6 = 10/12
X = 60/12
= 5

[@raya.pawley3563]

Thank you

[@larbibenmrad1968]

Thalès
12 / 6 = 10 / x
x = 5

[@Stylux-z1p]

6 + 6 = 12
12 / 10 = 6 / x --> proportion
12x = 10 · 6
12x = 60
12x/12 = 60/12
x = 5 ✅
pythagorean theorem : c² = a² + b²
the hypotenuse :
c² = 5² + 6²
c = √[5² + 6²]
c = √[25 + 36]
c = +/_√[61]
c = √61✅

[@dellenrules]

This takes way too long.
Make a Square/rectangle and find the area.
12 x 10 / 2 =60
The answer becomes viable in the bottom half. Has the same area size as top and bottom together.
6 x (10)=60
So X+X= 10 therefore X is 5.😊

[@pandurangaraonimmagadda9966]

x/6= 10/12, x=5

[@narenmenon6906]

you had to calculate, eh?

[@panlomito]

x : 6 = 10 : 12 so x = 6 x 10 / 12 = 5
Deja vu !

[@pierrebringmans4274]

12÷10=1.2
6÷1.2=5
Answer is 5

[@jsfoster100]

5

[@chrismcgowan3938]

It has to be x=5

[@Charles-db3kr]

Jusr turn it into a rectangle. The rectangle side is 10. Half of that is 5. It is not complicated

[@geogeo6071]

10 is to 12 as x is to 10. Solve for x.

[@josephlaura7387]

X=5

[@narenmenon6906]

similar triangles... therefore ans is 5

[@spunstricken9065]

5

[@Dr_piFrog]

x = 5