Recall that we are given triangles of the form
We are told that an appropiate triangle must have the following property
[tex]\frac{a}{b}=\frac{1}{12}[/tex]
We will calculate that number for each triangle and check if it is or not appropiate
Triangle A
For this triangle we have a=1 and b=12, so we have
[tex]\frac{a}{b}=\frac{1}{12}[/tex]
so triangle A is appropiate.
Triangle B
For this triangle we have a=40 and b=30. So we have
[tex]\frac{40}{30}=\frac{4\cdot10}{3\cdot10}=\frac{4}{3}[/tex]
which is not equivalent to the fraction 1/12. Thus, triangle B is not appropiate.
Triangle C
For this triangle we have a=10 and b=120. So we have
[tex]\frac{a}{b}=\frac{10}{120}=\frac{1\cdot10}{12\cdot10}=\frac{1}{12}[/tex]
Thus triangle C is also appropiate.
Triangle D
For this triangle we have a=1 and b=15. So we have
[tex]\frac{a}{b}=\frac{1}{15}[/tex]
which is not equivalent to the fraction 1/12. Thus, triangle D is not appropiate.
Triangle E
We are given the value of a=2. However, we need to find the value of b. We are given the following triangle
For this triangle, using the pythagorean theorem we have
[tex]15^2=2^2+b^2=4+b^2[/tex]
So, by subtracting 4 on both sides we get
[tex]b^2=15^2\text{ -4}[/tex]
So, applying the square root, we have
[tex]b=\sqrt[]{15^2\text{ -4}}=\sqrt[]{221}=14.8660[/tex]
Thus, this means that
[tex]\frac{a}{b}=\frac{2}{14.8660}[/tex]
which is not equivalent to the fraction 1/12. Then triangle E is not appropiate.
