Question

in the right triangle shown, df = ef = 3. how long is de? choose 1 answer: a 3√2 b 3√3 c 6 d 6√2 e 9

Explanation:

Step1: Apply Pythagorean theorem

In right triangle \( \triangle DFE \), by Pythagorean theorem, \( DE^{2}=DF^{2}+EF^{2} \). Given \( DF = 3 \), \( EF = 3 \).

$$ DE^{2}=3^{2}+3^{2}=9 + 9=18 $$

Step2: Solve for \( DE \)

Take square root on both sides: \( DE=\sqrt{18}=\sqrt{9\times2}=3\sqrt{2} \).

Answer:

A. \( 3\sqrt{2} \)