Answer to Question #23575 in Geometry for Tyshelle

Question

The area of a square garden is 200 m². How long is the diagonal?

Answer 1

The area of a square garden equal:S=a^2
S - area of the garden
a - length of the side of the garden
then:
a =Sqrt[S]
The length of the diagonal equal (due to Pythagorean theorem):
d^2= a^2 + a^2
Therefore:
d = Sqrt[2]*a
d = Sqrt[2]*Sqrt[S] = Sqrt [2S] = Sqrt [400 m^2] = 20 m
Answer: 20 m