Question

A diagonal of a square parking lot is 70 meters. How do you find, to the nearest meter, the length of a side of the lot?

Answer 1

Side to the nearest meter = 49 meters.

Explanation:

The diagonal divides the square into 2 congruent right triangles that share the diagonal as the common hypotenuse. Using the Pythagoras Theorem:
`c^2=a^2+b^2`
But since the square has 4 equal sides the 2 right triangles are also Isosceles, so we can rewrite the above equation as:
`a^2+a^2=c^2`
Or:
`2a^2=c^2`
Substitute 70 meters for c we get:
`2a^2=(70)^2`
Solving for a:
`a^2 = 4900/2=2450`
`a=sqrt2450=35sqrt2` meters
`a~~49.497474` meters,
Rounding to the nearest meter we get:
`a=49` meters