# 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?

Oct 25, 2015

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:
$2 {a}^{2} = {c}^{2}$
Substitute 70 meters for c we get:
$2 {a}^{2} = {\left(70\right)}^{2}$
Solving for a:
${a}^{2} = \frac{4900}{2} = 2450$
$a = \sqrt{2450} = 35 \sqrt{2}$ meters
$a \approx 49.497474$ meters,
Rounding to the nearest meter we get:
$a = 49$ meters