Question

what is the value of x in the triangle? a. 4 b. 2 c. 4√2 d. 2√2

Explanation:

Step1: Identify the triangle type

It's a 45 - 45-90 right - triangle. In a 45 - 45-90 triangle, the ratio of the sides is $1:1:\sqrt{2}$, where the legs are of equal length and the hypotenuse is $\sqrt{2}$ times the length of a leg.

Step2: Set up the relationship

Let the length of each leg be $x$ and the hypotenuse be $h$. The formula for the hypotenuse of a 45 - 45-90 triangle is $h = x\sqrt{2}$. Given $h = 4$.

Step3: Solve for $x$

We have $4=x\sqrt{2}$. Then $x=\frac{4}{\sqrt{2}}$. Rationalize the denominator: $x=\frac{4\sqrt{2}}{2}=2\sqrt{2}$.

Answer:

D. $2\sqrt{2}$