Question

A hamster has made holes in opposite corners of a rectangular living room. The living room is 16 feet by 12 feet. If the hamster runs straight from one hole to the other, how far will it run?

a) 16 feet
b) 20 feet
c) 28 feet
d) 32 feet

Answer 1

To determine the distance the hamster will run across the rectangular living room, the Pythagorean theorem is used to find the diagonal, resulting in a distance of 20 feet.

Step-by-step explanation:

The student has asked about the distance a hamster will run if it goes straight from one hole to another across a rectangular living room which measures 16 feet by 12 feet. To find this distance, we can treat the problem as finding the diagonal of a rectangle. By applying the Pythagorean theorem, we can calculate the diagonal as follows:

1. Let one side of the rectangle be 'a' (16 feet) and the other side be 'b' (12 feet).
2. The diagonal 'd' forms a right-angled triangle with sides 'a' and 'b'.
3. According to Pythagorean theorem, d^2 = a^2 + b^2.
4. Thus, d^2 = (16)^2 + (12)^2 = 256 + 144 = 400.
5. Take the square root of both sides, d = √400 = 20 feet.

Therefore, the hamster will run 20 feet from one hole to the other when it runs straight across from opposite corners of the room.