Question

question 6 of 10
what is the length of \\( \overline { b c } \\) in the right triangle below?

a. 82
b. 98
c. 6724
d. 1512
e. \\( \sqrt { 3624 } \\)
f. 14

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle \(ABC\) with \(\angle A = 90^{\circ}\), by the Pythagorean theorem \(BC^{2}=AB^{2}+AC^{2}\). Given \(AB = 18\) and \(AC = 80\).
So, \(BC^{2}=18^{2}+80^{2}\).

Step2: Calculate \(AB^{2}\) and \(AC^{2}\)

\(18^{2}=18\times18 = 324\), \(80^{2}=80\times80=6400\).
Then \(BC^{2}=324 + 6400\).

Step3: Sum the values

\(BC^{2}=324+6400=6724\).

Step4: Find \(BC\)

Take the square root of \(BC^{2}\), \(BC=\sqrt{6724}\). Since \(82\times82 = 6724\), so \(BC = 82\).

Answer:

A. 82