i'm a mathlete in class but I have huge problems with geometry. Can u help me answer this math 5th grade??????

Question

Please state the solution if you want.
1) A child glued together 42 cubes with 1 cm edges to form a solid rectangular brick. i fthe perimeter of the base is 18 cm, what is the height of the brick?

Here's another geometry related question:
2) How many segments have their endpoints that are vertices of a cube?

Out of 100 items, that's the only two things I do not understand and all of them are geometry related. Please explain your answer. thank you, I really wanna ace this one to cover up my quite average grades back then.

yah, I agree with you, question #2 is icomplete.

Answer 1

1) The height is 3 cm, and the base is 2 cm x 7 cm. This can be figured out by first trying out a height of 1 cm, then of 2 cm, then of 3 cm, before the solution is discovered. Good old trial and error.

2) My best guess is that the segments are those forming a cube, being connected at the vertices. Obviously, there's 12 of them, just count them. Now, the maximum number of lines that can be drawn between vertices of a cube is 12 more on the faces of the cube (6 crossed pairs), and 3 more diagonals going through the center of the cube, making 27 in all. The question is not clear for which answer it wants.

Answer 2

For the first question:
The amount of cubes used for the base is the perimeter of the base minus four. This is because every cube will have one edge contribute to the perimeter except for the corner cubes which will have two edges contribute to the perimeter. So the base is made up of 14 cubes. Since it is a rectangular brick, which should be referred to as a rectangular prism, and there are 42 cubes in all the rectangular prism is 3 cubes high as 42/14=3. So the height is 3 cm. Trial and error would obviously work but in order to learn math, as you are a mathlete and I once was, you must understand the process. Not all questions can be solved in a timely manner by trial and error so you must learn the process of solving problems.

Although helmets answer will give you the correct answer for this question if the numbers were larger it would be impractical to factor those numbers. Remember that the answer is not the important thing in math the thought process into getting the correct answer, a thought process which can be extended to every question of this type, is the goal.

For the second question:
All of the line segments, remember line SEGMENTS, not lines as they do not have endpoints as another responder did not allude to, of a cube have their endpoints as vertices of a cube. There are 12 line segments that make up a cube. Remember that although this answer is what you are looking for there is really no correct answer. An infinite amount of line segments can make up a cube. If you run into an ambiguous question like this in a competition and you do not get the answer correct you can dispute this as the question is poorly written.

Answer 3

1) Ok, perimeter is twice the length plus twice the width, so the length plus the width must be 9. The volume of the brick is 42 cubes. 42 = 2*3*7. 9 = 2 + 7, leaving only the 3 for the height of the brick.

2) There are 4 lines for the top square, 4 lines for uprights, and 4 lines for the bottom square. Adding them up you get 12.

Answer 4

if you cal x,y and z the dimension of the brick you get
x+y = 9(perimeter)
x*y*z = 42( volume of the 42 cubes.So z=42/x*y must be a whole number so x*y is a divider of 42
But 42 = 2*3*7 (prime number discomposition) so you get

x+y=9
x*y= 2,3,7,6,14,21
You must solve this system with each of the 6 nimber trying to get as solution a whole number
Lets try with x*y=14
x*(9-x)=14========> x^2-9*x+14=0 Solving this 2nd degree eq
you get x=2 or 7and y =:7 or 2 (Wht soever)so z must be 3.
the high of the brick is 3 cm