Question

the pythagorean theorem in three d

rebecca has a gerbil that lives in a cage in the shape of a rectangular prism. she wants to put a
ramp in the cage to give her gerbil exercise. the cage has a length of 70 cm, a width of 35 cm,
and a height of 50 cm. how long does the ramp need to be to fit diagonally in the cage? round
the answer to the nearest tenth. (1 point)

82.3 cm
100.3 cm
86.2 cm
108.1 cm

Explanation:

Step1: Find the diagonal of the base

Use the Pythagorean theorem for the base (\(l = 70\) cm, \(w=35\) cm).
\(d_{base}=\sqrt{l^{2}+w^{2}}=\sqrt{70^{2}+35^{2}}=\sqrt{4900 + 1225}=\sqrt{6125}\)

Step2: Find the space - diagonal

Use the Pythagorean theorem again with \(d_{base}\) and height \(h = 50\) cm.
\(d=\sqrt{d_{base}^{2}+h^{2}}=\sqrt{6125+50^{2}}=\sqrt{6125 + 2500}=\sqrt{8625}\approx92.9\)

Answer:

\(92.9\) cm (corresponds to the first option \(92.9\) cm)