Question #20

Question

The height of a box is 8cm and the total surface area of the box is 114cm^2. Find the length of a side of the base of the box if the base is a square 

Answer 1

Hi Lauren,

Here's what we know:  We have a box in which the top and bottom are square; therefore the area of the top + the area of the bottom is x² + x², or 2x².  the area of each of the sides of the box is 8 times x, or 8x. Since there are 4 sides, the total area of the sides is 4(8x) or 32x cm.

 

the surface area is 114 cm²

 

therefore, 2x² + 32x= 114

 

Solving for x by factoring, you get (x-3)(x + 19) = 0   (you will also get thesame answer by using the quadratic formula

 

therefore, x = 3, x = -19; but the only answer that makes sense is x = 3; the length of any side of the base of the box is 3 cm

 

Hope this helps