Question

an architecture firm is designing a pavilion in the shape of a square pyramid. they plan to add a string of lights of length ( b ) (in meters) to each of the edges that meet at the top. in the figure, the edge with length ( b ) shows the placement of one string of lights. (the figure is not drawn to scale.)
(a) find ( a ).
( a=square mathrm{m} )
(b) use your answer to part (a) to find ( b ), the length of one string of lights. round your answer to the nearest tenth of a meter.
( b=square mathrm{m} )

Explanation:

Step1: Find the value of \(a\)

The base of the right - triangle for finding \(a\) has a length of \(9\) m (half of the \(18\) m side of the square base). Using the Pythagorean theorem \(a=\sqrt{12^{2}+9^{2}}\).

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Step2: Find the value of \(b\)

Now, to find \(b\), we consider another right - triangle with legs \(a = 15\) m and \(9\) m. Using the Pythagorean theorem \(b=\sqrt{15^{2}+9^{2}}\).

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Answer:

a) \(a = 15\) m
b) \(b\approx17.5\) m