Page 142 - Calculus Workbook For Dummies

126 Part III: Differentiation

3. A right triangle is placed in the first quad- 4. You’re designing an open-top cardboard
rant with its legs on the x and y axes. Given box for a purveyor of nuts. The top will be
that its hypotenuse must pass through the made of clear plastic, but the plastic-box-
point (2, 5), what are the dimensions and top designer is handling that. The box
area of the smallest such triangle? must have a square base and two card-
board pieces that divide the box into four
Solve It sections for the almonds, cashews, pecans,
and walnuts. See the following figure. Given
that you want a box with a volume of 72
cubic inches, what dimensions will mini-
mize the total cardboard area and thus
minimize the cost of the cardboard? What’s
the total area of cardboard?

Solve It