Question

Two sides of a triangle have the same length.the third side measures 6m less than twice the common length.the perimeter of the triangle is 10m.what are the lengths of all three sides?

Answer 1

Let the two sides be represented by x,

Let the third side be 2x - 6 since it is 6m less than twice the common length.

The perimeter of the triangle is,

`x+x+2x-6=\text{Perimeter}`

Given that the perimeter of the triangle is 10m, let us solve for x,

`\begin{gathered} x+x+2x-6=10 \\ 4x-6=10 \\ \text{collect like terms,} \\ 4x=10+6 \\ 4x=16 \end{gathered}`
`\begin{gathered} x=(16)/(4) \\ x=4m \end{gathered}`

Let us now get the length of the three sides of the triangle,

`\begin{gathered} x=4m\text{ for the first length} \\ x=4m\text{ for the second length} \\ 2x-6=2(4)-6=8-6=2m \\ 2x-6=2m\text{ for the third length} \end{gathered}`

Hence, the length of the three sides are 4m, 4m, and 2m.