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

Answer 1

The answer is 3 units

Answer 2

Answer: In the oblique rectangular prism with a base square, the slanted edge length is 3 units longer compared to its perpendicular height.

Answer. Third option: 3 units

Solution:

Volume of the oblique rectangular prism: V=539 cubic units

Square base, with edge a=7 units

Slanted edge length: s=14 units

How many units longer is the slanted edge length of the prism, 14, compared to its perpendicular height?

s-h=?

Perpendicular height of the prism: h=14 units

V=Ab h

Area of the base: Ab

Ab=a^2

Replacing a by 7 units in the formula above:

Ab=(7 units)^2

Ab=49 square units

V= Ab h

Replacing V by 539 cubic units and Ab by 49 square units in the formula above:

539 cubic units = (49 square units) h

Solving for h: Dividing both sides of the equation by 49 square units:

(539 cubic units) / (49 square units) = (49 square units) h / (49 square units)

11 units = h

h= 11 units

s-h=14 units-11 units

s-h=3 units