SAT High School

~A certain rectangular prism has a height of h inches, a width that is 3 inches less than its height, and a length that is 4 inches more than its height. Ifthe area ofthe base of the prism is 60 square inches, what is the volume of the prism, in cubic inches?

Answers

Answer 1

Answer:

Volume = 480 cubic inches

Explanation:

We have the following relationships to work with

width w = h -3

length l = h + 4

area of base of prism a = l x w = 60  (1)

area of base in terms of h = (h-3)(h+4) =h² -3h + 4h -12 (2)

Setting (1) = (2) gives

h² + h -12 =60

h² + h -72 = 0

Factoring the LHS we get

(h+9)(h-8) = 0

The solutions for h are

h + 9 = 0 ==> h = -9

h - 8 = 0 ==> h = 8

Since h cannot be negative, h = 8 inches

Volume = base area x h = 60 x 8 = 480 cubic inches

Note

We do not have to calculate length and width separately, but if so,

w = 8 -3 = 5

l = 8 + 4 = 12

Related Questions

Critically discuss three ways in which physical activities could improve your quality of life

Answers

Answer:

hola

Explanation:

What element MOST defines a fairy tale?

1. involving real-world historical figures

2. involving a person of royal station (e.g., prince)

3. involving actual fairies (or their regional equivalent)

4. involving some magical force

Answers

Answer:

4. involving some magical force

Explanation:

If not 4, then try 2

The answer is 4 b/c all fairytales have some sort of magic
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