Question

A square piece of cardboard is used to make an open box. The four shaded squares are cut from the corners, and the sides are folded up along the dotted lines. The base is a square with side length of
x
inches, and the height of the box is
10
inches.

The expression
(
x
+
20
)
(
x
+
20
)
−
4
(
100
)
represents the area of cardboard used.

image




Which interpretation of the expression is TRUE?



A.
(
x
+
20
)
represents a side length of the parts of the box that are not the base.

B.
4
(
100
)
represents the area of cardboard used for the sides of the box, not including the base.

C.
4
(
100
)
represents the area of the original large square piece of cardboard before any cuts were made.

D.
(
x
+
20
)
represents a side length of the original large square piece of cardboard before any cuts were made.

Answer 1

Answer: D.

Reason: The box height 10 in means 10-by-10 squares were cut from each corner. The original cardboard side = base x plus two cut widths = x + 2(10) = x + 20, so (x+20) is the original square's side length. 4(100) = 4(10^2) are the areas of the four cut-out squares (removed), and (x+20)^2 − 4(100) = original area − removed area.