The side of a square is measured as 98 inches with a possibl

The side of a square is measured as 9.8 inches with a possible error of 1/15 inch. Using these measurements, determine the interval containing the possible areas of the square. (Round your answer to three decimal places.)

Solution

Side of square x = 9.8 inch

error in measurement dx = 1/15 inch

Area of square A = x²

==> A = 9.8² = 96.04 inch²

error in area dA = 2x dx

==> dA = 2(9.8)(1/15) = 98/75 = 1.3067 inch²

limits area A +/- dA

==> 96.04 - 1.3067 inch² <= area <= 96.04 + 1.3067 inch²

==> 94.733 inch² <= area <= 97.347 inch²