Question

A box is formed by cutting square pieces out of the corner of a rectangular piece of a "3x5" notecard. The sides are then folded up to box form.

(a) Write the function that expresses the area of the bottom of the box as a function of the length of the side of one of the square pieces.

(b) How large should x be in order for the area of the bottom of the box to equal 10in^2? Round your answer to the nearest hundredth.

Answer 1

Function:

Area of the bottom of the box = 4x^2 - 16x + 15

x = 0.34 in

Explanation:

This is a draw of what I understood.

You have a notecard of 3x5 in^2 and you cut squares with "x" side from the corners.

Once you fold the notecard to form a box, the sides of the bottom of the box are 3 - 2x and 5 - 2x because each side will lose the length of 2 sides of the square.

(a) Area of the bottom of the box:

A = (3 - 2x ) ( 5 - 2x ) = 15 - 6x - 10x + 4x^2 = 4x^2 -16x + 15

(b) You replace A for 10 in the expression from (a):

10 = 4x^2 - 16x + 15

0 = 4x^2 - 16x + 5

Solving that you get 2 values of x:

x = 0.34 in

x = 3.66 in

It cant be 3.66 because you are cutting 2 x from each side of the rectangle and the sides are 3 and 5, so you cant cut 7.32 from it. Leaving the only valid answer x = 0.34 in