Question

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

Answer 1

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.