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Question

During the development stage of a new rectangular keypad for a security system, it was decided that the area of the rectangle should be 228 square centimeters and the perimeter should be 62 centimeters. Find the dimensions of the keypad.

Answer 1

Area = 228 = LW

Perimeter = 2(L+W) = 62

2L + 2W = 62

2L = 62-2W

L = 31-W

LW = 228

(31-W)W = 228

31W -W^2 = 228

W^2 -32W +228 = 0

W^2 -32W + 16^2 = 16^2-228

(W-16)^2 = 256-228 = 28

W-16 = sqr28

W =16 + or - 2sqr7 = about 16+ or - 5.3

W = about 21.3 or 10.7

L= 228/21.3 or 228/10.7 = 21.3 or 10.7

dimensions are 10.7 by 21.3, approximately

exact dimensions are 16+2sqr7 by 16- 2sqr7

(16+2sqr7)(16-2sqr7) = 256-28= 228

10.7x21.3 = 227.91.