Question

A rectangular football pitch is 100 m long and 70 m wide. What is the length of a diagonal of the football pitch? Explain how you worked out your answer. . Show all your working.​

Answer 1

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Answer 2

To find the length of the diagonal of a rectangular football pitch, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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 other two sides. In this case, the diagonal of the football pitch forms the hypotenuse of a right-angled triangle.

Here's how to work it out:

1. The length of the football pitch is 100 meters.
2. The width of the football pitch is 70 meters.

Now, you can consider these measurements as the two sides of a right-angled triangle, where the diagonal is the hypotenuse. Let's label the length as "a" and the width as "b."

a = 100 meters (length of the pitch) b = 70 meters (width of the pitch)

Now, using the Pythagorean theorem:

c² = a² + b²

c² = (100 meters)² + (70 meters)²

c² = 10,000 + 4,900

c² = 14,900

To find the length of the diagonal (c), take the square root of both sides:

c = √14,900

c ≈ 122.07 meters

So, the length of the diagonal of the football pitch is approximately 122.07 meters.