Question

question 4
the diagram shows a section of
the zoo where two paths meet at
a right angle. there are plans to
construct a new path as shown
by the dotted line. what will be
the length of the new path?
16.900 m
85 m
170 m
130 m

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem states that for a right - triangle \(a^{2}+b^{2}=c^{2}\), where \(a = 50\) m and \(b=120\) m, and \(c\) is the length of the hypotenuse (new path).
$$a^{2}+b^{2}=c^{2}$$
$$50^{2}+120^{2}=c^{2}$$

Step2: Calculate \(a^{2}\) and \(b^{2}\)

Calculate \(50^{2}=2500\) and \(120^{2}=14400\).
$$2500 + 14400=c^{2}$$
$$16900=c^{2}$$

Step3: Find \(c\)

Take the square root of \(16900\). Since \(c>0\), \(c=\sqrt{16900}\).
$$c = 130$$

Answer:

\(130\) m