Question

Find the value of x. Express your answer in simplest radical form.

Answer 1

D

x=5*sqrt(2)/2

Explanation:

since it is a right triangle, and one of the other angles is 45, we know that the last angle must also be 45 since the 3 interior angles must be 180

then using pythagroem theorem

sqrt(a^2+b^2)=c

sqrt(x^2+x^2) = 5

square both sides

x^2+x^2=25

2x^2=25

x^2=25/2

square root both sides

x= sqrt(25/2)=5/sqrt(2)

rationalize the demonominator by multiplying by sqrt(2)/sqrt(2)

x=5*sqrt(2)/2