A board, 32 cm long is cut into three pieces such that the second piece is twice as long as the first and the third is 7 cm longer than the second.

Find the length of the shortest piece.

Let x = the shortest piece.

x + 2x + 2x + 7 = 32

thank you sooo much

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5 To find the length of the shortest piece, let's first represent the lengths of the three pieces:

Let's call the length of the first piece x cm.
According to the given information, the second piece is twice as long as the first piece, so its length is 2x cm.
Similarly, the third piece is 7 cm longer than the second piece, so its length is (2x + 7) cm.

Now, we know that the total length of the board is 32 cm. Therefore, the sum of the three pieces' lengths should be equal to 32 cm:

x + 2x + (2x + 7) = 32

Simplifying the equation:

5x + 7 = 32

Subtracting 7 from both sides:

5x = 25

Dividing both sides by 5:

x = 5

Now that we have found the length of the first piece, we can substitute this value into the original equation to find the lengths of the second and third pieces:

First piece: x = 5 cm
Second piece: 2x = 2(5) = 10 cm
Third piece: 2x + 7 = 2(5) + 7 = 17 cm

Therefore, the length of the shortest piece is 5 cm.