Question

question 24 of 28 what is the length of (overline{gh}) in the right - triangle below? a. 1296 b. 1746 c. 36 d. (sqrt{1746})

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs. Here, if the hypotenuse is $GF = 39$ and one leg is $FH=15$, and we want to find the other leg $GH$. Let $GH = x$. Then $x^{2}+15^{2}=39^{2}$.

Step2: Rearrange the formula to solve for $x$

$x^{2}=39^{2}-15^{2}$. Calculate $39^{2}=39\times39 = 1521$ and $15^{2}=15\times15 = 225$. So $x^{2}=1521 - 225=1296$.

Step3: Find the value of $x$

Take the square - root of both sides. $x=\sqrt{1296}=36$.

Answer:

C. 36