# Answer to Question #23575 in Geometry for Tyshelle

Question #23575

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

Expert's answer

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

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

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