Question

The three sides of a triangle are n. 4n + 1, and 5n -- 8. If the perimeter of the triangle is 93 cm, what is the length of each side?Separate multiple entries with a comma.

Answer 1

Given:

The three sides of a triangle are, n, 4n + 1, and 5n - 8.

The perimeter is 93.

To find the length of each side:

The formula of the perimeter of a triangle is,

`\begin{gathered} P=a+b+c \\ 93=n+4n+1+5n-8 \\ 93=10n-7 \\ 100=10n \\ n=(100)/(10) \\ n=10 \end{gathered}`

So, the length of the sides are,

`\begin{gathered} n=10 \\ 4n+1=4(10)+1\Rightarrow41 \\ 5n-8=5(10)-8\Rightarrow42 \end{gathered}`

Therefore, the length of the sides of a triangle are 10, 41, and 42.