<span>The distance from the vertex to the centroid is twice the distance from the centroid to the side.
This means that 3x + 5 = 2 * (2x)
</span><span>3x + 5 = 4x
x = 5
Source:
http://www.1728.org/trictr.htm
</span>
7h+3s=27.95 subtract 7h from both sides
3s=27.95-7h divide both sides by 3
s=(27.95-7h)/3
Then we are told:
5h+4s=23.4, using s found above makes this equation become:
5h+4(27.95-7h)/3=23.4 multiply both sides by 3
15h+4(27.95-7h=70.2 perform indicated multiplication on left side
15h+111.8-28h=70.2 combine like terms on left side
-13h+111.8=70.2 subtract 111.8 from both sides
-13h=-41.6 divide both sides by -13
h=$3.20
We have to calculate the volume of the right rectangular prism.
lenght=4 1/2 in=(4+1/2) in=9/2 in
width=5 in
height=3 3/4 in=(3+3/4) in=15/4 in
Volume (right rectangular prism = lenght x width x height.
volume=9/2 in * 5 in * 15/4 in=675/8 in³
we calculate the volume of this little cube.
volume=side³
volume=(1/4 in )³=1/64 in³
Now, we calculate the number of small cubes are needed to fit the right rectangular pris by the rule of three.
1 small cube----------------1/64 in³
x---------------------------------675/8 in³
x=(1 small cube * 675/8 in³) / 1/64 in³=5400 small cubes.
Answer: we need 5400 small cubes to fit the right rectangular prism.
