Question

If the lengths of the legs of a right triangle are 4 and 8, what is the length of the hypotenuse?A. 4√3B. 32C. 12D. 4√5

Answer 1

To solve this question, we will make use of the Pythagorean theorem.

The pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

From this theorem, we have that

`\begin{gathered} \text{hypotenuse}^2=opposite^2+adjacent^2 \\ \\ \text{hyp}^2=opp^2+adj^2 \end{gathered}`

From here, we have that

`\begin{gathered} \text{hyp}^2=opp^2+adj^2 \\ \\ \text{hyp}^2=4^2+8^2 \\ \\ \text{hyp}^2=16+64 \\ \\ \text{hyp}^2=80 \\ \\ \text{hyp = }\sqrt[]{80} \\ \\ \text{hyp = }\sqrt[]{16*5} \\ \\ \text{hyp = }\sqrt[]{16}*\sqrt[]{5} \\ \\ \text{hyp = 4}*\sqrt[]{5} \\ \\ \text{hyp = 4}\sqrt[]{5} \end{gathered}`

Therefore, option D is the correct answer.