What is x in the diagram below

A. 10 squareroot 14

B.2squareroot10

C.10squareroot4

D.20squareroot3

Guest Jul 25, 2019

#1**+1 **

\(\text{well we can get a few equations using the Pythagorean theorem}\\ \text{Let the left hand unlabeled leg be $a$ and the right hand one be $b$}\\ x^2+4^2=a^2\\ x^2+16=a^2\\~\\ a^2+b^2=(10+4)^2= 14^2=196\\~\\ x^2+10^2=b^2\\ x^2+100=b^2\)

\(\text{We can add the first and third equations}\\ x^2+16+x^2+100=a^2+b^2\\ 2x^2 + 116 = a^2+b^2\\~\\ \text{and note this equals the left hand side of the second equation}\\ 2x^2+116 = 196\\~\\ 2x^2=80\\ x^2=40\\ x=\sqrt{40}=2\sqrt{10}\\~\\ \text{choice B}\)

.Rom Jul 25, 2019