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

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

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct