Question

Help if possible.
A box is to be formed by cutting square pieces out of the corner of a rectangular piece of a 3" x 5" notecard as shown below. The sides are then folded up to form a box ( see attachment).
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 10 in^2? Round your answer to the nearest hundredth.

Answer 1

a ) Length = 5 - 2 x
Width = 3 - 2 x
The area of the bottom:
A = L  x  W = ( 5 - 2 x ) ( 3 - 2 x ) = 15 - 10 x - 6 x + 4 x² = 
= 4 x² - 16 x + 15
b ) 4 x² - 16 x + 15 = 10
4 x² - 16 x + 5 = 0
x = (16 - √(256 - 80))/ 8 = ( 16 - 13.266 ) / 2
x = 0.34 in