A square floor has a diagonal of 30 feet. What is the closest estimate of the perimeter, in feet, of the floor?

Explanation

Step 1: Use the Diagonal Formula for a Square

For a square with side length $s$, the diagonal $d$ is given by:

$$d = ssqrt{2}$$

Substituting $d = 30$

$$30 = ssqrt{2}$$

Step 2: Solve for s

$$s = frac{30}{sqrt{2}}$$

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

$$s = frac{30sqrt{2}}{2} = 15sqrt{2}$$Approximating 

$sqrt{2} approx 1.414$

$$$$s≈15×1.414=21.21

Step 3: Calculate the Perimeter

The perimeter $P$ 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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