Question

question 5 of 24 look at the figure below and calculate the length of side y. a. 12 b. 8.5 c. 6 d. 17

Explanation:

Step1: Identify the triangle type

This is 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 $a$ and the hypotenuse be $c$. We know $c = 12$ and $y$ is a leg. Using the Pythagorean theorem $a^{2}+a^{2}=c^{2}$ for a 45 - 45 - 90 triangle. Since $y$ is a leg and if we assume the length of the leg is $y$, and $c = 12$, then $2y^{2}=12^{2}$.

Step3: Solve for $y$

First, expand the right - hand side: $2y^{2}=144$. Then divide both sides by 2: $y^{2}=72$. Take the square root of both sides: $y=\sqrt{72}=\sqrt{36\times2}=6\sqrt{2}\approx 8.5$.

Answer:

B. 8.5