# math

posted by .

At the ruins of Caesarea, archaeologists discovered a huge hydraulic concrete block with a volume of 945 cubic meters. The block's dimensions are x meters high by 12x - 15 meters long by 12x - 21 meters wide. What is the height of the block?

• math -

remember , volume = lwh

x(12x-15)(12x-21) = 945
simplifying a bit

x(3)(4x - 5)(3)(4x-7) = 945
x(4x-5)(4x-7) = 105
16x^3 -48x^2 +35x - 105=0
by grouping ...
16x^2(x - 3) + 35(x-3) = 0
(x-3)(16x^2 + 35) = 0
x = 3 or x^2 = -35/16 , which is not real

so the only real solution is x = 3

so the block is 3 m high,

• math -

How do you get 105?

• math -

I divided both sides by 9
945รท9=105
notice the (3)(3) is gone on the left side

## Similar Questions

1. ### Math

Did I do this right? A cage with a volume of 27 cubic meters, if the sides are in whole meters only and the width is 3 meters, what are the possible dimensions for the length and height?

how many cubic meters of dirt are in a hole 6 meters long,2 meters wide, and one meter deep?
3. ### Math

A rectangular swimming pool is 7 meters longer then it is wide. It is surrounded by a concrete walkway 1.5 meters wide. The area of the walkway is 120 meters squared. What are the dimensions of the pool?
4. ### math

The swimming pool that Calvin goes to has dimensions 20 meters long, 8 meters wide and 3 meters deep. What is the volume of water (in m3) that the swimming pool contains?
5. ### Algebra 2

At the ruins of Caesarea, archaeologists discovered a huge hydraulic concrete block with a volume of 945 cubic meters. The block's dimensions are x meters high by 12x - 15 meters long by 12x - 21 meters wide. What is the height of …
6. ### Math Multiplying Fractions

A swimming pool in the shape of a rectangular prism is 50 meters long 25 meters wide and 3 meters deep. A liter is the same as 0.001 cubic meters. How many liters of water are needed to completely fill the pool?
7. ### math

A pool must be 25 meters long and 3 meters deep and the room is only 10 meters wide can u still build a pool that will hold 800 cubic meters of water and why
8. ### Algebra

The underside of a concrete bridge forms a parabolic arch that is 32 meters wide at the water level and twelve meters high in the center. The road (top of the bridge) is forty eight meters wide, and the minimum thickness of the concrete …
9. ### Math

A rectangular room is 4 meters wider than its high and it is 8 meters longer than its wide. the total Ares of the wall is 512 square meters. Find the dimensions of the room.
10. ### Math

a rectanglular form is 3.5 meters long,2 2/5 meters wide and 2.5 meters deep.Tory filled it full of cement,leaving 25 centimeters space at the top.How many cubic meters of cement did Tory use?

More Similar Questions