Question 577617: I am a rectangular prism, so I have a height (h), a width (w) and a depth (d). Here are your clues to determining each of my dimensions...my depth is 3 more units than my width, my height is 1.5 units less than my depth, and the sum of my 3 dimensions is slightly > 25 units. Finally, my volume is 595 cubic units while my surface area is 429 square units.
What are my 3 dimensions? List the depth, height and width
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! I am a rectangular prism, so I have a height (h), a width (w) and a depth (d).
:
Write an equation for each statement:
:
" depth is 3 more units than my width,"
d = w + 3
or
w = (d-3)
:
"height is 1.5 units less than my depth,"
h = (d-1.5)
:
"the sum of my 3 dimensions is slightly > 25 units."
h + w + d > 25
:
" volume is 595 cubic units"
h*w*d = 595
:
"surface area is 429 square units."
2(h*w) + 2(h*d) + 2(w*d) = 429
:
Replace h and w in the sum equation
h + w + d > 25
(d-1.5) + (d-3) + d > 25
3d - 4.5 > 25
3d > 25 + 4.5
3d > 29.5
d > 29.5/3
d > 9.833
d = 10 is the depth
then
w = 10-3
w = 7 is the width
and
h = 10-1.5
h = 8.5 is the height
:
Find vol with these values
8.5 * 7 * 10 = 595, checks out
:
Check the surface area
2(8.5*7) + 2(8.5(10) + 2(7*10) =
119 + 170 + 140 = 429
:
Summarize: h = 8.5; w = 7; d = 10
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