Jake has a 3 foot long peice of wood that he wants to make into a triangular frame. He cuts a peice off of the board that is 1 foot 5 inches long. From the remaining board he cuts off another peice that is 7 inches long. He now has 3 peices of wood. Will he be able to fit 3 peices together to make a triangle? Explain
No, he can't. Since his first cut was in the middle, making one more cut cannot make two sides that exceed the length of the longest side. To form a triangle, no side can have a length that equals or exceeds the sum of the lengths of the other two sides.
drwls probably made an arithmetic error.
Jake starts with 36 inches, cuts off 17 inches, leaving 19 inches.
From that he cuts 7 inches, leaving 12
so his 3 pieces are 17, 7, and 12 inches.
The sum of any two of these exceeds the third side, so the triangle is possible. (ignoring any lengths lost due to the cuts)
Yeah he can
bec 1foot = 12inches
so the piece of wood has 3*12 36 inch long
so the first piece = 12+5=17 inch
the second piece = 7 inch
so the last piece = 36-(7+17)=12 inch
so do the inequality of triangle (the sum of two sides must be greater than the remaining side)
to shortcut time and effort sum the smallest sides and see if the sum is greater than the biggest side
(12+7)>?17
19>17
then it can be triangle
To determine if Jake can fit the three pieces together to make a triangle, we need to check if the sum of any two sides of the triangle is greater than the remaining side.
Let's first convert the measurements into a consistent unit. Since we have feet and inches, it's better to convert everything to inches:
3 feet = 36 inches
1 foot 5 inches = 17 inches
7 inches = 7 inches
Now, let's analyze the three pieces:
1. The original piece was 36 inches long.
2. Jake cut off a piece of 17 inches.
3. From the remaining board (19 inches), he cut off another piece of 7 inches.
Let's check the possible combinations:
1. The original piece (36 inches) combined with the first cut-off piece (17 inches):
36 + 17 = 53 inches
2. The original piece (36 inches) combined with the second cut-off piece (7 inches):
36 + 7 = 43 inches
3. The first cut-off piece (17 inches) combined with the second cut-off piece (7 inches):
17 + 7 = 24 inches
Now let's analyze the possible combinations:
1. 53 inches is greater than the remaining piece (19 inches), so these two pieces can be combined to form a triangle.
2. 43 inches is greater than the remaining piece (19 inches), so these two pieces can be combined to form a triangle.
3. 24 inches is less than the remaining piece (19 inches), so these two pieces cannot be combined to form a triangle.
Based on the analysis, Jake can combine the original piece with either of the cut-off pieces, but the two cut-off pieces cannot be combined to form a triangle. Thus, Jake will not be able to fit all three pieces together to make a triangle.