Question

Question 4 of 10What is the value of x in the figure below? In this diagram, AABD - ACAD.10B1625O A.B.165O C. 8OD. 15OE. 160OO F. 16

Answer 1

The first step to find the answer to this question is to find the missing leg of the greatest triangle. To do it we have to apply pythagorean theorem:

`\begin{gathered} l=\sqrt[]{16^2-10^2} \\ l=\sqrt[]{256-100} \\ l=\sqrt[]{156} \end{gathered}`

Now, use this value and the pythagorean theorem (again) to state two equations that are useful to find the height of the two smallest triangles. For one of them it would be:

`h=\sqrt[]{10^2-x^2}`

For the other one:

`h=\sqrt[]{\sqrt[]{156}^2-(16-x)^2}`

Make both equation equal and solve for x:

`\begin{gathered} \sqrt[]{10^2-x^2}=\sqrt[]{\sqrt[]{156}^2-(16-x)^2} \\ 10^2-x^2=\sqrt[]{156}^2-(16-x)^2 \\ 100-x^2=156-(256-32x+x^2) \\ 100-x^2=-100+32x-x^2 \\ 200=32x \\ x=(200)/(32) \\ x=(25)/(4) \end{gathered}`

It means that the correct answer is A. 25/4.