Question

Find the value of x. Round the answer to the nearest tenth, if needed.

A.
4.8
B.
5.1
C.
8.2
D.
9.5

Answer 1

c. 8.2is correct it a bit bigger than both

Answer 2

The answer is D

Explanation:

In order to determine the "x" value, we use the thales theorem.

This theorem makes equalities between the sides and angles of a right triangle. I have attached an image that shows the equality we need.

Let me explain the image:

Let AD be perpendicular to BC. We have ∠ABC=∠DBA and ∠BAC=∠BDA=90°

So, hence by Thales theorem we have

:

`(AB)/(BD)=(BC)/(BA)\\AB^2=BC*BD`

In this case, AB=x ; BD=7 and BC=13.

Then:

`AB^2=BD*BC\\x^2=7*13\\x^2=91\\x=9.5`

Finally, the "x" value is 9.5