What type of number can be written as a fraction p/q where p and q are integers and q is not equal to 0
2 answers:
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Answer:
Step-by-step explanation:
Notice that is a right triangle where its hypotenuse is
. We can also see that
. For this we must use the Pythagorean Theorem.
Recall:
The Pythagorean Theorem states that if you have a right triangle, the principal square root of the sum of the squares of each leg is the length the hypotenuse.
We can see that and
First notice that the triangle with sides 
and the triangle with sides 
are similar. This is true because the angle between sides 
in the smaller triangle is clearly 
, while the angle between sides 
in the larger triangle is clearly 
. So the triangles are similar with sides corresponding to 
, respectively.
Now both triangles are
, which means there's a convenient ratio between its sides. If the length of the shortest leg is 
, then the length of the longer leg is 
and the hypotenuse has length 
.
Since
is the shortest leg in the larger triangle, it follows that 
, so 
Now both triangles are
Since