Question

review the illustration below and answer the question that follows.
a
5m
12m
b
jayden wants to get from his house (point a) to the library around the corner (point b). however, he cannot go through his
how long would his walk be if he could go directly from point a to point b?
10 meters
11 meters
12 meters
13 meters

Explanation:

Step1: Identify the triangle type

The triangle is right - angled (since it has a right angle as seen from the illustration with legs 5m and 12m). We can use the Pythagorean theorem, which states that for a right - angled triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here, \(a = 5\) m and \(b=12\) m.

Step2: Apply the Pythagorean theorem

Substitute \(a = 5\) and \(b = 12\) into the formula: \(c^{2}=5^{2}+12^{2}\). Calculate \(5^{2}=25\) and \(12^{2}=144\). Then \(c^{2}=25 + 144=169\).

Step3: Find the value of \(c\)

Take the square root of both sides: \(c=\sqrt{169}=13\) m.

Answer:

13 meters