Question

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Answer 1

We use the Pythagorean Theorem: 6² - 4² = TQ², TQ = 2√5 ≈ 4
The length of each side of the square is about 4 units and the length of it's diagonal is about 4√2 ≈ 6 units.
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Hope this helps!

Answer 2

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Find TQ :
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a² + b² = c²
4² + TQ² = 6²
TQ² = 6² - 4²
TQ² = 36 - 16
TQ² = 20
TQ = 2√5 units  or 4.47 units (nearest hundredth)

The length of TQ is 2√5 units

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Find the diagonal of the square :
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a² + b² = c²
(2√5)² + (2(√5)² = c²
c² = 20 + 20 
c² = 40
c = √40
c = 2√10 units or 6.32 units (nearest hundredth)

The diagonal of the square is 2√10 units