A rectangle park measures 300 ft by 400 ft. A sidewalk runs diagonally from one corner to the opposite corner. Find the length of the sidewalk.

What is the Theorem of Pythagoras?

a squared + b squared = c squared

A rectangle park measures 300 ft by 400 ft. A sidewalk runs diagonally from one corner to the opposite corner. Find the length of the sidewalk.

To find the length of the sidewalk, we can use the Pythagorean theorem. The theorem states that 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 other two sides.

In this case, the rectangle forms a right triangle, with the sides of the rectangle as the other two sides. So, let's label the sides of the rectangle as follows:

A = 300 ft (length of the rectangle)
B = 400 ft (width of the rectangle)
C = length of the sidewalk (hypotenuse)

Using the Pythagorean theorem, we have the equation:

A^2 + B^2 = C^2

Substituting the values we know:

300^2 + 400^2 = C^2

Simplifying:

90000 + 160000 = C^2

250000 = C^2

To solve for C, we need to find the square root of both sides:

√250000 = √C^2

500 = C

Therefore, the length of the sidewalk is 500 ft.