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A square floor has a diagonal of 30 feet. What is the closest estimate of the perimeter, in feet, of the floor?
  1. 45
  2. 60
  3. 85
  4. 96
Explanation
Step 1: Use the Diagonal Formula for a Square

For a square with side length ss, the diagonal dd is given by:

d=s2d = ssqrt{2}

Substituting d=30d = 30

30=s230 = ssqrt{2}

Step 2: Solve for s
s=302s = frac{30}{sqrt{2}}

Multiply numerator and denominator by 2sqrt{2} to rationalize:

s=3022=152s = frac{30sqrt{2}}{2} = 15sqrt{2}Approximating 

2≈1.414sqrt{2} approx 1.414

s≈15×1.414=21.21
Step 3: Calculate the Perimeter

The perimeter PP of a square is:


P approx 4 times 21.21 = 84.84
P=4s
P≈4×21.21=84.84
The closest estimate is 85.

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