Question

The perimeter of the triangle below is 91 units. Find the length of the side QR. write your answer without variables.

Answer 1

Given:

The perimeter of the triangle, P=91.

The sides of the triangle are,

PR=4z

QR=z+3

PQ=5z-2.

The perimeter of the triangle can be expressed as,

`\begin{gathered} P=PR+QR+PQ \\ P=4z+z+3+5z-2 \\ P=10z+1 \end{gathered}`

Now, put P=91 in the above equation to find the value of z.

`\begin{gathered} 91=10z+1 \\ 91-1=10z \\ 90=10z \\ (90)/(10)=z \\ 9=z \end{gathered}`

Now, the length of the side QR can be calculated as,

`\begin{gathered} QR=z+3 \\ QR=9+3 \\ QR=12 \end{gathered}`

Now, the length of QR is 12 units.