Another geomerty problem!!?

Question

A 12 foot board needs to be cut into 3 pieces that are in a ratio of 3 to 2 to 1. What is the lenght of the longest piece???

Answer 1

x+2x+3x=12
6x=12

x=2
2x=4
3x=6

longest piece is 6 feet

Answer 2

2 4 6

Answer 3

Let the shortest piece be represented by x. Then the next piece, which is twice as long, is 2x. The longest piece is 3/2 as long as the second piece, so it is (3/2)(2x) = 3x feet long.

Now, just add all these variable terms together to get:

x + 2x + 3x = 12
6x = 12
x = 2

So the longest piece is 3(2) = 6 feet long.

Add up the lengths as a check:

2(1) + 2(2) + 3(2) = 2 + 4 + 6 = 12

Now check to see if we have the correct ratios:

2x/x = 2/1
3x/2x = 3/2

So our lengths and our ratios check out, meaning the solution is correct, and the longest piece is 6 feet long.

Answer 4

The ratio is:

3 feet time x to 2 feet times x to 1 foot times x = 12 feet

Equate and solve for x.

3x + 2x + x = 12

6x = 12

x = 2

NOW, take the value of x (which is 2) and plug it into

3x and 2x to find the longest piece.

Here are the 3 pieces:

Piece 1 is x = 2 feet

Piece 2 is 3(2) = 6 feet

Piece 3 is 2(2) = 4 feet

The answer is?????

6 feet is the longest piece.

Guido

Answer 5

ok so this is what you do -

3x + 2x + x = 12
6x = 12
x = 2

so youve figured out what x =s, now you just plug it into the numbers.

3 (2) + 2 (2) + 2 = 12
6 + 4+ 2 = 12
12 = 12

so now youve checked AND youve found out that the longest piece is 6 feet. i hope you get it! :-)

Answer 6

6 - 4 - 2

Answer 7

First = 6 : Longest
Second = 4
Third = 2

Answer 8

x + y + z ...12
----------- = -----
3 + 2 + 1 ....6

x/3 = 12/6
x = 2 . 3
x = 6

y/2 = 12/6
y = 2 . 2
y = 4

z/1 = 12/6
z = 2
Answer: The lenght of the longest piece is 6 ft.
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