Question

question 3 (3 points)
listen
in a right triangle, one leg measures 4 inches and the other leg measures 6 inches.
what is the length of the hypotenuse in inches?
a) 52
b) \\( \sqrt { 52 } \\)
c) 10
d) \\( 2 \sqrt { 13 } \\)

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 4\) and \(b = 6\), and hypotenuse \(c\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\).
Substitute \(a = 4\) and \(b = 6\) into the formula: \(c^{2}=4^{2}+6^{2}\).
Calculate \(4^{2}=16\) and \(6^{2}=36\), then \(c^{2}=16 + 36=52\).

Step2: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{52}\).
Simplify \(\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}\).

Answer:

D. \(2\sqrt{13}\)