Question

use the diagram of a square pyramid to answer the question. what is the length of the slant height, l? a. 3 in. b. 9 in. c. √39 in. d. √41 in. e. √89 in.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, one leg \(a = 5\) in and the other leg \(b\) is calculated as \(\frac{8}{2}=4\) in (since the base of the right - triangle formed is half of the side length of the square base of the pyramid). Let the slant height \(L\) be the hypotenuse.

Step2: Substitute values into the formula

Substitute \(a = 5\) and \(b = 4\) into \(a^{2}+b^{2}=L^{2}\). So, \(L^{2}=5^{2}+4^{2}\).

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Step3: Solve for \(L\)

Take the square root of both sides. \(L=\sqrt{41}\) in.

Answer:

D. \(\sqrt{41}\) in.