Questions: Find the value of x. A. 4√2/2, B. 4 C. 4√2 D. 4√3

Solution Steps

The given triangle is a 45°-45°-90° triangle. In such triangles, the lengths of the legs are equal, and the hypotenuse is \( x\sqrt{2} \) where \( x \) is the length of each leg.

Given that the hypotenuse is \( 4\sqrt{2} \), we can use the relationship for a 45°-45°-90° triangle: \[ \text{Hypotenuse} = x\sqrt{2} \]

Set the hypotenuse equal to \( 4\sqrt{2} \): \[ x\sqrt{2} = 4\sqrt{2} \]

Divide both sides by \( \sqrt{2} \): \[ x = 4 \]

Final Answer