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?

1 Answer
Oct 25, 2015

Answer:

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