Answer:
D. 12
Step-by-step explanation:
We have been given a diagram of a triangle. We are asked to find the value of y for our given triangle.
First of all, we will find 3rd side of larger triangle using Pythagoras theorem.
[tex]\text{3rd side}^2=16^2-8^2[/tex]
[tex]\text{3rd side}^2=256-64[/tex]
[tex]\text{3rd side}^2=192[/tex]
[tex]\text{3rd side}^2=192[/tex]
We will use geometric mean (leg) theorem to solve our given problem.
[tex]\text{3rd side}^2=y\times 16[/tex]
[tex]192=y\times 16[/tex]
[tex]\frac{192}{16}=\frac{y\times 16}{16}[/tex]
[tex]y=12[/tex]
Therefore, the value of y is 12 and option D is the correct choice.
