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Harrizon [31]
3 years ago
7

Given two sides with lengths 34 and 14, which of these lengths would NOT work for the third side of a triangle? 18, 34, 44, 22,

40
Mathematics
1 answer:
Bas_tet [7]3 years ago
7 0
Two sides are 34 and 14.

The third side can't be longer than (34 + 14) = 48, because the 34 and the 14
together could not reach from one end of it to the other. 

The third side also can't be shorter than 20, because the 20 and the 14 together
could not reach from one end of the 34 to the other.

So 18 doesn't work. (18 + 14) = 32 ... they couldn't cover the 34 .
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Now, let's break down the equation in English. We'll use #1, #2, #3, #4, and #5 as stand-ins for the five integers just so we can get things set up, then we'll replace them with the expressions we came up with in the first part. Starting from the beginning of the statement, let's translate words to symbols:

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Putting that all together, we get the equation

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We can now start to simplify our equation to find n (the first integer) and the rest will follow easily from that. I'll start by focusing on the left side. We can distribute and combine like terms like so:

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Dealing with the right, we can get rid of some redundant parentheses and carry out the same process:

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Our simplified equation now becomes

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Subtracting 5n from either side:

8 = 4n - 36

Adding 36 to either side:

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And dividing either side by 4:

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We now know that our first integer is 11, which means that our 5 consecutive integers are 11, 12, 13, 14, and 15.

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