an architecture firm is designing a pavilion in the shape of a square pyramid. they plan to add a string of…

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 = 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 = m

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 = 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 = m

Answer

Explanation:

Step1: Find the base - length of the right - triangle for finding (a)

The base of the right - triangle for finding (a) has length (12) m (half of the side of the square base (24) m) and the height of the pyramid is (9) m. We use the Pythagorean theorem (a=\sqrt{9^{2}+12^{2}}).

Step2: Calculate (a)

[ \begin{align*} a&=\sqrt{81 + 144}\ &=\sqrt{225}\ &=15 \end{align*} ]

Step3: Find (b) using (a)

We consider another right - triangle with one leg of length (12) m and the other leg of length (a = 15) m. We use the Pythagorean theorem (b=\sqrt{15^{2}+12^{2}}).

Step4: Calculate (b)

[ \begin{align*} b&=\sqrt{225+144}\ &=\sqrt{369}\ &\approx19.2 \end{align*} ]

Answer:

(a) (a = 15) m (b) (b\approx19.2) m