Question

what is the length of x in this 45-45-90 triangle?
(1 point)
○ 4
○ 4√3
○ 4√2
○ 8

Explanation:

Step1: Recall 45-45-90 triangle ratios

In a 45-45-90 triangle, the legs are equal, and the hypotenuse \( h \) is related to a leg \( l \) by \( h = l\sqrt{2} \). Here, one leg is 4, so the other leg \( y = 4 \) (since it's a 45-45-90 triangle, legs are equal). The hypotenuse is \( x \).

Step2: Apply the hypotenuse formula

Using the formula \( h = l\sqrt{2} \), with \( l = 4 \), we get \( x = 4\sqrt{2} \).

Answer:

\( 4\sqrt{2} \) (corresponding to the option with \( 4\sqrt{2} \))