Xai4jTondnPetens3te Xai4jTondnPetens3te
  • 21-11-2016
  • Mathematics
contestada

write the area A of a square as a function of its perimeter P. ...?

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JcAlmighty
JcAlmighty JcAlmighty
  • 23-11-2016
The answer is A = P²/16

The perimeter P of a square is sum of its sides s: P = s + s + s + s = 4s
The area A of a square with side s is: A = s * s  = s²

Step 1: Solve s from the formula for the perimeter.
Step 2: substitute s from the formula for the perimeter into the formula for the area.

Step 1:
P = 4s
s = P/4

Step 2:
A = s²
s = P/4
A = (P/4)²
A = P²/4²
A = P²/16
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