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The area of the floor of a rectangular room is 195 m2

. One wall is a rectangle

with area 120 m2 and another wall is a rectangle with area 104 m2

. If the
dimensions of the room are all integers, what is the volume of the room?

I also cannot understand this when I was on a test and really wanted too the above one is from my homework and this one is from a test I gave last week


Forty-two cubes with 1 cm edges are glued together to form a solid rectangular
block. If the perimeter of the base of the block is 18 cm, what is the height?

 Apr 11, 2020
edited by kijijij  Apr 11, 2020
 #1
avatar+30087 
+4

Let floor length be x and floor width be y. Then:

 

x*y = 195.   (1)

x*h = 120.   (2)

y*h = 104.   (3)

 

(2)*(3):   x*y*h2 = 120*104 so h2 = 120*104/195 (using (1));  h2 = 64;  h = 8

 

Volume of room = x*y*h = 195*8 = 1560 m3

 Apr 11, 2020
 #2
avatar+30087 
+2

Let there be x*y cubes on the bottom. Perimeter = 2(x + y)

 

2(x + y) = 18;   x + y = 9

 

Possibilities

x = 8,  y = 1.  8 cubes on the bottom. But 42/8 is not a whole number, so not this.

 

x = 7,  y = 2.  14 cubes on the bottom. 42/14 = 3, so height = 3 cubes = 3 cm.

 

x = 6, y = 3.   18 cubes on the bottom.  42/18 not a whole number.

 

x = 5, y = 4.    20 cubes on the bottom. 42/20 ...etc.

 Apr 11, 2020

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