The printed matter on a 12 by 24 centimeter page of a book must cover 64 square centimeters. If all margins are to be the same width, how wide should the margins be?
The printed matter on a 12 by 24 centimeter page of a book must cover 64 square centimeters. If all margins are to be the same width, how wide should the margins be?
So we need a few formulas to start.
The area of a rectangle is
We know the area
We also know that the length is five more than the width so
and that the width is W.
Now we evaluate the area formula to get
So now using the zero product priciple we set each factor equal to zero to get
and
Since we are talking about the width of a frame the negative solution doesn't make sense so we are left with the width of the frame is 7 in.
Good luck.
Let x be the size of the margins. Then the length of the printed matter is and the width is
Using the Area formula from the above post we get
we can factor a 2 out of each factor on the left hand side to get
now we can reduce the equation by dividing both sides by 4 to get
Now we expand the right hand side to get
So we get that x=14 or x=4
We reject the first solution becuase if we plug it back into the original equation the length and width are negative so x =4 is the solution.
The margins should be 4cm