Question

in the right triangle △rst, the legs rs and st have lengths 6 cm and 8 cm, respectively. what is the length, in centimeters, of the hypotenuse rt?
a. 7
b. 9
c. 10
d. 12

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). Here \(a = 6\) and \(b=8\).
So, \(6^{2}+8^{2}=c^{2}\).

Step2: Calculate the squares

\(6^{2}=36\) and \(8^{2}=64\). Then \(36 + 64=c^{2}\).

Step3: Sum the values

\(36+64 = 100\), so \(c^{2}=100\).

Step4: Find the square root

Take the square root of both sides: \(c=\sqrt{100}\).

Answer:

C. 10