Question

liam keeps his pet lizard in a tank shaped like a right rectangular prism. the dimensions of the tank are shown.
liam puts a stick in the tank for his lizard to climb. the stick has a length of ( s ) feet as shown in the diagram. what is the approximate length of the stick to the nearest tenth of a foot?
a ( 3.6 ) feet
b ( 4.5 ) feet
c ( 5.0 ) feet
d ( 5.4 ) feet

Explanation:

Step1: Find the length of the base diagonal

Use the Pythagorean theorem for the base (length \(l = 4\) ft, width \(w=3\) ft).
The base - diagonal \(d_1\) is given by \(d_1=\sqrt{4^{2}+3^{2}}\).

$$d_1=\sqrt{16 + 9}=\sqrt{25}=5$$

Step2: Find the length of the space - diagonal (stick length \(s\))

Use the Pythagorean theorem again with the height \(h = 2\) ft and the base - diagonal \(d_1=5\) ft.
The space - diagonal \(s\) is given by \(s=\sqrt{d_1^{2}+h^{2}}\).

$$s=\sqrt{5^{2}+2^{2}}=\sqrt{25 + 4}=\sqrt{29}$$

$$s\approx5.4$$

Answer:

D. \(5.4\) feet