Question

The area of a square garden is 200 m^2. How long is the diagonal?

Answer 1

Answer:

Step-by-step explanation:

A square has equal length sides.  The area of a square is side times side, or

$A=s^2$

The diagonal of a square is the hypotenuse of the right triangle that is formed using 2 sides of the square.  This right triangle is a 45-45-90.  Now let's back to the area.  If the area is 200 meters squared, then filling that in to the formula gives us

$200=s^2$ and simplifying to get the length of a side, gives us

$s=10\sqrt{2}$

But in finding the length of the diagonal, we will use Pythagorean's Theorem, which will use the s-squared value instead of s:

$c^2=200+200$ and

$c^2=400$  so

c = 20

That's the length of the diagonal.