Question

1. maria walks 10 feet due north and then walks 4 feet due west. she then heads straight back to her original point, taking the diagonal path. what is the length of the diagonal path, to the nearest tenth of a foot?

a 10.2 ft
b. 10.8 ft
c. 11.2 ft
d. 11.8 ft

Explanation:

Step1: Identify the problem type

This is a right - triangle problem. Maria's two paths (north and west) form the two legs of a right - triangle, and the diagonal path is the hypotenuse. Let \(a = 10\) (north) and \(b=4\) (west).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\), where \(c\) is the hypotenuse. Substitute \(a = 10\) and \(b = 4\) into the formula: \(c=\sqrt{10^{2}+4^{2}}=\sqrt{100 + 16}=\sqrt{116}\).

Step3: Calculate the value of \(\sqrt{116}\)

\(\sqrt{116}\approx10.8\) (using a calculator, \(\sqrt{116}=\sqrt{4\times29}=2\sqrt{29}\approx2\times5.385 = 10.77\approx10.8\))

Answer:

B. \(10.8\) ft