Question

an oblique rectangular prism with a square base has a volume of 539 cubic units. the edges of the prism measure 7 by 7 by 14 units. how many units longer is the slanted edge length of the prism, 14, compared to its perpendicular height? 1 unit 2 units 3 units 4 units

Explanation:

Step1: Find the base - area of the prism

The base is a square with side length $a = 7$ units. The base - area $B$ of a square is given by $B=a^{2}$. So, $B = 7^{2}=49$ square units.

Step2: Use the volume formula to find the perpendicular height

The volume formula of a prism is $V = B\times h$, where $V$ is the volume, $B$ is the base - area, and $h$ is the perpendicular height. We know that $V = 539$ cubic units and $B = 49$ square units. Rearranging the formula for $h$, we get $h=\frac{V}{B}$. Substituting the values, $h=\frac{539}{49}=11$ units.

Step3: Find the difference between the slanted edge length and the perpendicular height

The slanted edge length is 14 units and the perpendicular height is 11 units. The difference $d$ is $d=14 - 11 = 3$ units.

Answer:

3 units