Question

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

Answer 1

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√(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.