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The perimeter of a triangle is 51 cm. The lengths of its sides are x cm, x + 2 cm, and x + 4 cm. What is the length, in cm, of the longest side of the triangle Enter your response Here

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The perimeter of the triangle is the sum of the lengths of its sides; therefore, since the side lengths are x, x + 2, and x + 4 cm and the perimeter is 51 cm, we have


x+(x+2)+(x+4)=51

Simplifying the left-hand side of the above gives


3x+6=51

subtracting 6 from both sides gives


3x=45

Finally dividing both sides by 3 gives


x=15.\text{ }

And we have the value of x! We now go on to find the value of the side lengths


x=15.\text{ }
\begin{gathered} x+2=15+2 \\ x+2=17 \end{gathered}
\begin{gathered} x+4=15+4 \\ x+4=19. \end{gathered}

Hence, the side lengths are 15cm, 17cm, and 19cm.

User Scott Chu
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