Answer:
Approximately [tex]5.7[/tex] inches
Step-by-step explanation:
The crossbar and two given lengths form a right triangle. We know this because we see a right angle marked on the diagram in between the two given sides.
In this case, we have a right triangle with legs of [tex]4[/tex] and [tex]4[/tex], and we need to find the hypotenuse. By the Pythagorean Theorem ([tex]a^{2} +b^{2} =c^{2}[/tex], where [tex]a[/tex] and [tex]b[/tex] are the legs and [tex]c[/tex] is the hypotenuse), we get:
[tex]4^{2} +4^{2} =c^{2}[/tex]
[tex]16+16=c^{2}[/tex] (Evaluate exponents)
[tex]32=c^{2}[/tex] (Combine like terms)
[tex]\sqrt{32}=\sqrt{c^{2}}[/tex] (Take the square root of both sides of the equation to get rid of [tex]c[/tex]'s exponent)
[tex]c=4\sqrt{2} ,c=-4\sqrt{2}[/tex]
The latter solution is an extraneous solution because the side lengths of a triangle cannot be negative. Therefore, the answer is [tex]4\sqrt{2} \approx 5.7[/tex] inches. Hope this helps!
