Question

a hallway is 100 feet long and 10 feet wide. if a piece of string stretches from one corner to the opposite corner, what is the length of the string? (round to the nearest tenth) 100.5 feet 120 feet 110.4 feet

Explanation:

Step1: Apply Pythagorean theorem

The hallway is a rectangle, so the diagonal (string length) $d$ follows $d = \sqrt{l^2 + w^2}$, where $l=100$ ft, $w=10$ ft.
$$d = \sqrt{100^2 + 10^2}$$

Step2: Calculate squared terms

Compute $100^2$ and $10^2$, then sum.
$$d = \sqrt{10000 + 100} = \sqrt{10100}$$

Step3: Compute square root, round

Calculate $\sqrt{10100} \approx 100.4988$, round to nearest tenth.
$$d \approx 100.5$$

Answer:

100.5 feet