Question

A walkway along the diagonal of a square park is 4/5 miles long. what is the area of the park?

Answer 1

`(8)/(25)` square miles

Explanation:

The relationship between the side length (let it be s) of a square and its diagonal (let it be d) is given by:

`s=(d)/(√(2) )`

Since d is given as 4/5, we solve for s:

`s=(d)/(√(2) )\\s=((4)/(5))/(√(2) )\\s=(4)/(5√(2) )`

NOW, area of square is s^2 where s is the side length.

Area =
`s^2=((4)/(5√(2) ))^2=(16)/(50)=(8)/(25)`