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Inessa [10]
3 years ago
6

Makayla has two types of ropes. She wants to cut the ropes into pieces of the same length for butterfly knots. One is 84 inches,

the other is 116 inches.
Find the greatest possible length that she can cut for each piece, so that no rope will be left unused.
Mathematics
2 answers:
Lunna [17]3 years ago
6 0

Remark

If you want every piece you cut equal to the same length, you are talking about the GCF because both ropes have to be cut in such a way that all parts of the whole set of ropes are the same size.

Prime Factors of 84 and 116

84: 2 * 2 * 3 * 7

116: 2 * 2 * 29

The two 2s are all that is common.

So that means that the 84 inch length will give you 21 lengths that are 4 inches long and the 116 inch length will give you 29 lengths that are 4 inches long.

Pavel [41]3 years ago
3 0

In this problem, we are trying to find the greatest common factor, or the greatest amount that both values share. To find this, we will need to factor our values though prime factorization:

84 = 2^2 \cdot 7^1 \cdot 3^1

116 = 2^2 \cdot 29


We can see that the greatest value that we can find in both numbers is 2^2, or 4, meaning our answer is 4 inches.

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1.) \sqrt{13.341}  ≈ 3.652

2.) I would say something about how the A in front of cos in the equation would change to 90, rather than stay 75 (in the equation for the step by step), but it would be easier to just use the Pythagorean theorem.

Step-by-step explanation:

I think we may have the same class so hopefully this helps:

1.) a^2 = b^2 + c^2 - 2bccosA --> law of cosines formula.

   a^2 = 3^2 + 3^2 - 2(3)(3)cos(75) --> plugged in numbers; when you draw the triangle, the included angle would be A, and the opposite side would be a. B and b, and C and c are opposite each other. In this case, a is the hypotenuse.

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Good luck! :)

   

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