Arectangular park measures 300ft by 400ft. a sidewalk runs diagonally from one corner to the opposite corner. find the lunch of the sidewalk.

When we are given a line cutting diagonally from one corner of a rectangle to the opposite corner, we are given two triangles.

300ft

| /|
| / |
| / |
| / |400ft
| / |
| / |
|/ |


*not to scale

Now, using the right-angle trigonometry rule, we can find the hypotenuse (the diagonal line) which represents the footpath.

a^2 + b^2 = c^2

{where a is one side length, b is another side length, and c is the hypotenuse}

Thus, we make c the subject of the equation and substitute the other known values:

c^2 = 400^2 + 300^2
= 160,000 + 90,000
= 250,000

Now we move the 'squared' (^2) from the left hand side to the right hand side. When moving it across the equal sign (=) the result becomes the 'root' of itself:

c = _/250,000
= 500

Therefore, the length of the diagonal path is 500ft.