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 130 m
85 m 170 m
120 m
50 m

Explanation:

Step1: Identify right triangle sides

The two existing paths form the legs of a right triangle: $a = 120\ \text{m}$, $b = 50\ \text{m}$. The new path is the hypotenuse $c$.

Step2: Apply Pythagorean theorem

Use $c = \sqrt{a^2 + b^2}$

$$ c = \sqrt{120^2 + 50^2} $$

Step3: Calculate squared terms

$$ 120^2 = 14400,\ 50^2 = 2500 $$

Step4: Sum and take square root

$$ c = \sqrt{14400 + 2500} = \sqrt{16900} = 130 $$

Answer:

130 m