Question 213863: The perimeter of a square is 36 centimeters. Find the length of the diagonal. Found 2 solutions by drj, solver91311:Answer by drj(1380) (Show Source):
Step 1. Let P be the perimeter of a square which means adding up all four sides.
Step 2. Let s be the side of a square.
Step 3 Then 4s=36 or s=9 centimeters after dividing by 4 to both sides of equation.
Step 4. Use Pythagorean Theorem to find diagonal which says that the sum of the square of the legs (=s^2+s^2=2s^2) is equal to square of the hypotenuse (diagonal in this case and letting d be the diagonal).
Step 5. ANSWER: The length of diagonal is centimeters
I hope the above steps were helpful.
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Let represent the perimeter of any square. Then a side of that square must measure because all four sides of a square are equal in measure. The diagonal of a square is the hypotenuse of an isoceles right triangle where the legs are two adjacent sides of the square. Pythagoras then says the measure of the hypotenuse and therefore the measure of the diagonal is:
Simplify:
Substitute your perimeter value, do the arithmetic, and you have your answer. Leave it in radical form for the exact answer, or use your calculator to get a numerical approximation -- depending on what your instructor wants.
