Why Walking Across the Grass is Faster: Pythagoras Explained

Introduction: The Shortcut in the Park

30m

40m

You are standing at one corner of a park (Point A). You want to get to the opposite corner (Point C).

You could walk along the sidewalk: walk 30 meters East, turn left, and walk 40 meters North. Or, you could cut across the grass directly.

Intuition tells you the grass is faster. But how much faster? This isn't just a geometry problem; it's the Pythagorean Theorem ( $a^2 + b^2 = c^2$ ), the universe's formula for calculating shortcuts.

The Core Formula: $a^2 + b^2 = c^2$

a & b
The "Long Way" (Legs): Just the two sides that meet at a right angle (90°).
c
The Shortcut (Hypotenuse): The longest side, opposite the right angle. Always shorter than $a + b$ combined.

Park Shortcut Calculation

Sidewalk: 30m + 40m = 70 meters
Grass (c): $sqrt{30^2 + 40^2} = sqrt{900 + 1600} = sqrt{2500} = 50$ meters
Saved: 20 meters!

Real World Magic (Not Just for Exams)

1. The Builder's "3-4-5 Rule"

How do builders ensure a wall corner is perfectly 90° without a giant protractor?

Measure 3ft on one wall.
Measure 4ft on the other.
Measure the distance between them.

If it's exactly 5ft, the corner is perfect.

2. Is That TV Too Big?

TVs are sold by diagonal size (c). If you buy a 50" TV, will it fit in your 45" wide cabinet?

ext{Width} = \sqrt{50^2 - ext{Height}^2}

You need the Pythagorean Theorem in reverse to know the actual width and height!

Ready to Cut Corners?

Whether you're building a deck, coding a game (calculating distance between players), or just trying to get home faster, this formula is your best friend.