Question

1. dyani is 1.8 meters tall and wants to be able to stand inside her new tent. should she buy the tent shown? tent features: - 3.4 cubic meters - square floor with 8.4 m perimeter - height clearance $59

Explanation:

Step1: Find the side length of the square floor

The perimeter of a square is \(P = 4s\), where \(s\) is the side - length. Given \(P=8.4\) m. Then \(s=\frac{P}{4}=\frac{8.4}{4}=2.1\) m.

Step2: Find the area of the square floor

The area of a square is \(A = s^{2}\). Substitute \(s = 2.1\) m, so \(A=(2.1)^{2}=4.41\) \(m^{2}\).

Step3: Find the height of the tent

The volume of a rectangular - based pyramid (tent) is \(V=\frac{1}{3}Ah\), where \(A\) is the base area and \(h\) is the height. Given \(V = 3.4\) \(m^{3}\) and \(A=4.41\) \(m^{2}\). Then \(h=\frac{3V}{A}\). Substitute \(V = 3.4\) and \(A = 4.41\), \(h=\frac{3\times3.4}{4.41}=\frac{10.2}{4.41}\approx2.31\) m.

Answer:

Since the height of the tent (\(h\approx2.31\) m) is greater than Dyani's height (\(1.8\) m), she should buy the tent.