let the margin be x cm wide all around
then length of printed area = 16-2x
width of printed area = 10-2x
(16-2x)(10-2x) = 40
160 -52x + 4x^2 = 40
4x^2 - 52x + 120=0
x^2 - 13x + 30 = 0
(x-4)(x-9) = 0
x = 4 or x = 9, but x=9 would produce a negative length and width, so reject it
The margin should be 4 cm wide
the printed matter on a 10 by 16 centimeter page of a book must cover 40 square centimeters. if all margins are to be the same width, how wide should they be?
2 answers
(10-2x) (16-2x ) = 40
160-20x -32x + 4x^2 = 40
160- 52x+ 4x^2 = 40
4x^2 -52x + 160 - 40 = 0
4x^2 -52x + 120=0
4(x-10)(x-3) = 0
x = 10, 3
Check
(10-2(3))(16-2(3)) = 40
(10-6)(16-6) = 40
(4)(10) = 40
40 = 40
(10-2(10))(16-2(10) = 40
(10-20)(16-20) = 40
(-10)(-4) = 40
40 = 40
160-20x -32x + 4x^2 = 40
160- 52x+ 4x^2 = 40
4x^2 -52x + 160 - 40 = 0
4x^2 -52x + 120=0
4(x-10)(x-3) = 0
x = 10, 3
Check
(10-2(3))(16-2(3)) = 40
(10-6)(16-6) = 40
(4)(10) = 40
40 = 40
(10-2(10))(16-2(10) = 40
(10-20)(16-20) = 40
(-10)(-4) = 40
40 = 40