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# Hellp

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1. In the triangle shown, the side lengths are given below in terms of a real-valued variable \$x\$. Find the range of all possible values of \$x\$, writing your answer in interval notation.

2.One side of a triangle has length \$10\$, and the triangle has integer perimeter. What is the smallest possible perimeter of the triangle?

3.Two side lengths of a triangle are \$11\$ and \$17\$. What is the longest possible integer length of the third side of the triangle?

Jan 28, 2020

#1
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1. The set of possible x is [3,25].

2.  The smallest possible perimeter is 23.

3. The largest possible third side is 29.

Jan 28, 2020
#2
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Thanks!  I also need help with these problems:

Get lost guest  and put your effort into doing your own homework.

Jan 28, 2020
edited by Melody  Feb 3, 2020
#3
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I'm not certain what the "\$" on each side of "x" represent.

If you are just considering all real numbers for the possibile replacements for x in the triangle whose sides are x + 15, 2x + 15, and 4x + 15, then, since the sum of any two sides of a triangle must be greater than the third side, there are these three possibilities:

I.    (x + 15) + (2x + 15) > 4x + 15     --->     3x + 30 > 4x + 15     --->     15 > x        --->     x < 15

II.   (x + 15) + (4x + 15) > 2x + 15     --->     5x + 30 > 2x + 15     --->     3x > -15     --->     x > -5

III.  (2x + 15) + (4x + 15) > x + 15     --->     6x + 30 > x + 15       --->     5x > -15     --->     x > -3

The answer is (-3, 15)     [Using a value of -4 or -5 for x results in a side of the triangle being negative.]

Using "\$x\$ to refer to just "x", I can't get any possible of answers that work for questions 2 and 3.

Jan 28, 2020
#4
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I would appreciated if you put the latex into the latex translator.

Jan 29, 2020