Question

sidewalk shortcut
at the park, you walk 6 blocks north, then 8 blocks east to meet a friend.
later, your friend texts: \why didnt you just take the shortcut across the grass?\
questions:

1. what do you notice about the shape your walking path creates?
2. how might you figure out how long the shortcut is—without measuring it directly?

Explanation:

1. The walking path creates a right - angled triangle. This is because one side is north (vertical) and the other is east (horizontal), forming a right angle between them.
2. To find the length of the shortcut (the hypotenuse of the right - angled triangle) without direct measurement, we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - angled triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here, \(a = 6\) blocks and \(b=8\) blocks.

Answer:

1. The shape is a right - angled triangle.
2. Use the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\) where \(a = 6\) and \(b = 8\).