Raj 有 120 个棱长为 1 厘米的立方体。
他将所有这些立方体拼成一个长方体。
该长方体顶面的周长为 20 厘米。
长方体的每条边长都大于 3 厘米。 求该长方体的高。 答：... 厘米

1. Find the possible dimensions of the top rectangle.

Let the length and width of the top be $l$ cm and $w$ cm.

Perimeter of top $=20$ cm:
$2(l+w)=20$
$l+w=10$

Since each side length is greater than $3$ cm and the cuboid is made from $1$ cm cubes, $l$ and $w$ are whole numbers greater than $3$.

Possible top dimensions are:
$4\text{ cm} \times 6\text{ cm} \quad \text{or} \quad 5\text{ cm} \times 5\text{ cm}$

2. Use the volume to determine the height.

The total volume is $120\text{ cm}^3$.

For top dimensions $4\times 6$:
$\text{height}=\frac{120}{4\times 6}=\frac{120}{24}=5$

For top dimensions $5\times 5$:
$\text{height}=\frac{120}{5\times 5}=\frac{120}{25}=4.8$

But the cuboid is made from $1$ cm cubes, so the height must be a whole number. Hence the height is
$5\text{ cm}.$