5.) a gardener wants to divide a square piece of lawn in half diagonally. what is the length of the diagonal side of the square is 8 fr. leave your answer in simplest radical form.

diagonal ^2 = 8^2 + 8^2

diagonal ^2 = 64 + 64

diagonal ^2 = 128

diagonal ^2 = 64 * 2

diagonal ^2 = 8 * sq root (2)

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

The length of the diagonal side can be calculated by using Pythagoras theorem.

The length of the diagonal side is 8√2

Pythagoras theorem:

diagonal ² = opposite ² + adjacent ²

= 8² + 8²

= 64 + 64

diagonal ² = 128

find the square root of both sides

√diagonal ² = √128

diagonal = √2×64

= √2 × √64

= √2 × 8

= 8√2

Therefore, the length of the diagonal side is 8√2

Learn more about the Pythagoras theorem:

link

180-142=38 for the acute angle next to the entry

90+38=128

180-128=52

a=52

step-by-step explanation: