How to Use the Pythagorean Theorem to Find the Hypotenuse with Sides 50 yd and 40 yd

The Pythagorean theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that:

c² = a² + b²

where:

• c is the length of the hypotenuse (the side opposite the right angle),
• a and b are the lengths of the other two sides.

Given your problem, you have two sides of lengths 50 yards and 40 yards, and you want to find the length of side A which is the hypotenuse.

Step 1: Identify the sides

Let’s let side a = 50 yd, side b = 40 yd, and side c = A (the hypotenuse).

Step 2: Plug values into the formula

c² = a² + b²

A² = (50)² + (40)²

Step 3: Calculate squares

A² = 2500 + 1600 = 4100

Step 4: Find the square root to get A

A = √4100

A ≈ 64.03 yards

Final answer:

The length of side A (the hypotenuse) is approximately 64.03 yards.