i need help solving a math word problem

Question

Harry's publishing company wants to design a page that has a 0.75 inch border on the left, a 1.5 inch border on the top and borders on the bottom and right of 1 inch. the borders are to surround 40 in² of print material. find the dimensions of the page that has the least area. what is the least area?

Answer 1

.75 border on left

1.5 border on top

1 border on bottom and right

area enclosed = 40 in^2

find dimensions with least area

area enclosed with least area has sides = 2sqr10

that means 1.75 added to width, and 2.5 added to height

dimensions are 2sqr10+1.75 by 2sqr10+2.5

= about 8.07 by 8.82

total area = about 8.07(8.82) = about 71.2

that's one idea

but since 2.5>1.75, it may be a lesser total area if the inside

enclosed dimensions had greater width than height

inside area = xy = 40, x =40/y

total area with borders = (1.75+y)(2.4+ 40/y) = 4.2 + 2.4y +70/y +40=

44.2 +2.4y +70/y

A'(y) = 2.4 -70/y^2 = 0

2.4y^2 = 70

y^2 = 70/2.4 = 700/24 = 29.1666...

y = sqr29.1666... = about 5.4

x = 40/5.4 = about 7.4

1.75+y = 7.15 inches wide

2.4+7.4 = 9.8 inches high

minimum total area = 7.15 x 9.8

= about 70.1 square inches

which is less than 71.2