Question

question 8 (1 point) a mason is using a right triangle to check a concrete basement floor to ensure that there are 90° angles in each corner. if the sides \\( \overline{ed} \\) and \\( \overline{fd} \\) measure 3 inches and 4 inches, then the distance between the endpoints of \\( \overline{et} \\) must be \\( \underline{\quad\quad} \\) that \\( \triangle def \\) is a right triangle.
options:
a 3
b 4
c 5
d 6
e 9

Explanation:

Step1: Identify triangle type

$\triangle DEF$ is a right triangle with right angle at $D$, so we use the Pythagorean theorem: $a^2 + b^2 = c^2$, where $a = 3$, $b = 4$, and $c = EF$.

Step2: Apply Pythagorean theorem

Substitute values: $3^2 + 4^2 = EF^2$. Calculate $9 + 16 = EF^2$, so $25 = EF^2$. Take square root: $EF = \sqrt{25} = 5$.

Answer:

5