Question

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Answer 1

Answer: $8\sqrt{2}\ feet$

Step-by-step explanation:

Given: The side length of a square garden = 8 ft.

Let x be the length of the diagonal of the garden.

Since all the angles of a square are right angle ($90^{\circ}$), then by constructing a diagonal into it, the square will get divide into two right triangles.

Then by Pythagoras theorem, we have

$x^2=8^2+8^2\\\Rightarrow\ x^2=64+64\\\Rightarrow\ x^2=128\\\Rightarrow\ x=\sqrt{128}\\\Rightarrow\ x=\sqrt{8\times8\times2}\\\Rightarrow\ x=8\sqrt{2}$

Hence, the length of the diameter=$8\sqrt{2}\ feet$

Answer 2

diagonal ^2 = 8^2 + 8^2

diagonal ^2 = 64 + 64

diagonal ^2 = 128

diagonal ^2 = 64 * 2

diagonal ^2 = 8 * sq root (2)

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Diagonal of a square = SqrRoot (2 * side^2)

Diagonal = SqrRoot (2 * 8^2)

Diagonal = SqrRoot (128)

SqrRoot (128) = SqrRoot (2 * 64) = SqrRoot (2) * 8

DIAGONAL = SqrRoot (2) * 8