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?

3 units

Solution:

V=539 cubic units

Square base, with edge a=7 units

Slanted edge length: s=14 units

V=Ab h

Ab=49 square units

539 cubic units = (49 square units) h

h = 11 units

s-h=14 units-11 units

s-h=3 units

3 units

Explanation:

Volume of an oblique rectangular prism with a square base = A*B*h

Where h = perpendicular height

From the question, Volume of an oblique rectangular prism with a square base = 539 cubic units

We were asked from the question to find how many units longer the slanted edge length of the prism, 14 is compared to its perpendicular height.

The first step is : Find the perpendicular height

Edges A = 7 units

Edges B = 7 units

Perpendicular height?

Hence,

539 = 7 * 7 * h

539 = 49h

h = 539 : 49

h = 11 units

Therefore, perpendicular height of the prism = 11 units

To find how many units longer, we would subtract the perpendicular height of the prism from the slanted edge length of the prism

= 14 units - 11 units

= 3 units.

Therefore the slanted edge length of the prism, 14, is 3 units longer compared to its perpendicular height.