Question

a scalene triangle has three unequal side lengths the side 1 is 9 yards longer than side 3 side 2 is three times as long as side 3 the total perimeter is 54 yards what are the lengths of the sides of the triangle

Answer 1

A scalene triangle has three unequal side lengths.

Let x be the length of the side 3

Side 1 is 9 yards longer than side 3

$Side\: 1=x+9$

Side 2 is three times as long as side 3

$Side\: 2=3x$

The total perimeter is 54 yards

$P=54\:$

Recall that the total perimeter is the sum of all three sides of the triangle.

$\begin{gathered} P=Side\: 1+Side\: 2+Side\: 3 \\ 54=(x+9)+(3x)+x \\ 54=x+x+3x+9 \\ 54=5x+9 \\ 5x=54-9 \\ 5x=45 \\ x=\frac{45}{5} \\ x=9 \end{gathered}$

So, the length of side 3 is 9 yards

$\begin{gathered} Side\: 1=x+9 \\ Side\: 1=9+9 \\ Side\: 1=18\: yd \end{gathered}$$\begin{gathered} Side\: 2=3x \\ Side\: 2=3(9) \\ Side\: 2=27\: yd \end{gathered}$

Therefore, the lengths of all three sides are

side 1 = 18 yards

side 2 = 27 yards

side 3 = 9 yards

The perimeter of the triangle is

$\begin{gathered} P=Side\: 1+Side\: 2+Side\: 3 \\ P=18+27+9 \\ P=54\: yd \end{gathered}$