Question

leg(height): 120 m
leg (base): 50 m

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?

130 m

16,900 m

170 m

85 m

Answer 1

To find the length of the new path, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In your case, the two legs of the triangle are:

- Height (leg): 120 m
- Base (leg): 50 m

Let \( c \) be the length of the new path (the hypotenuse):

\[
c^2 = 120^2 + 50^2
\]

Calculating:

\[
120^2 = 14400
\]
\[
50^2 = 2500
\]

Adding these results:

\[
c^2 = 14400 + 2500 = 16900
\]

Now, take the square root to find \( c \):

\[
c = \sqrt{16900} = 130 \, \text{m}
\]

So, the length of the new path is **130 m**.