Question

question 17 of 28 which of the following equations can be used to find the length of ef in the triangle below? a. (ef)^2 = 24^2+12^2 b. (ef)^2 = 24^2 - 12^2 c. ef = 24 + 12 d. ef = 24 - 12

Explanation:

Step1: Identify the right - triangle and relevant theorem

The triangle $\triangle DEF$ is a right - triangle with right angle at $\angle F$. We use the Pythagorean theorem which states that in a right - triangle, if the hypotenuse is $c$ and the two legs are $a$ and $b$, then $c^{2}=a^{2}+b^{2}$. Here, $DE = 24$ is the hypotenuse and $DF = 12$ and $EF$ are the legs. So, $DE^{2}=DF^{2}+EF^{2}$.

Step2: Rearrange the formula to solve for $EF$

We can rewrite the Pythagorean formula as $(EF)^{2}=(DE)^{2}-(DF)^{2}$. Substituting $DE = 24$ and $DF = 12$, we get $(EF)^{2}=24^{2}-12^{2}$.

Answer:

B. $(EF)^{2}=24^{2}-12^{2}$