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?
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
Let there be x*y cubes on the bottom. Perimeter = 2(x + y)
2(x + y) = 18; x + y = 9
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.