The lengths of a triangle are consecutive odd integers. The perimeter of the triangle is 33in. What is the length of the longest side?

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14-06-2018
Mathematics

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The lengths of a triangle are consecutive odd integers. The perimeter of the triangle is 33in. What is the length of the longest side?

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carlosego carlosego · Answer 1 · 2018-06-23T17:30:13+02:00

For this case, the first thing we must do is define a variable.
We have then:
x: shorter side length, odd number.
We now write the equation for the perimeter of the trig:
[tex]x + (x + 2) + (x + 4) = 33 [/tex]
From here, we clear the value of x.
We have then:
[tex]3x + 6 = 33 3x = 33 - 6 x = 27/3 x = 9[/tex]
Then, the length of the longest side is:
[tex]x + 4 = 9 + 4 = 13 [/tex]
Answer:
The length of the longest side is 33 inches.