Answer:
x = 5
Step-by-step explanation:
Pythagorean theorem
Hypotenuse² - Side 1² = Side 2²
Side² + side² = Hypotenuse²
More commonly written with
c² - a² = b²
c² - b² = a²
a² + b² = c²
b² + a² = c²
c represnts the hypotenuse
a and b are sides
Now with that in mind if we want to find the unsquared value we square root both sides, and because we're finding a side we'll use hypotenuse minus the given side.
[tex]\sqrt{c^2 - a^2} = \sqrt{b^2}[/tex]
where as b is the unknown side [tex]x[/tex]
PLUG AND SOLVE:
[tex]\sqrt{b^{2}} = \sqrt{x^2} =\sqrt{13^2-12^{2}} = \sqrt{(13*13)- (12*12)} = \sqrt{169-144} = \sqrt{25}[/tex]
so,
[tex]\sqrt{x^2} = \sqrt{25}[/tex]
thus
[tex]x = \sqrt{25} = 5[/tex]
Hope this helps,
- J.M.Jamon
Pennsylvania State University
Full-Time B.S.CE. Undergrad
