Question

There is a small table is 54 in. create an equation to find the value of n.

Answer 1

Given in the question

`\text{Area}_(RECTANGLE)=54in^2`

The length of the rectangle is

`l=3(n-1)=3n-3`

The breadth of the rectangle is

`b=n+2`

The formula for the Area of a rectangle is

`\begin{gathered} \text{Area}_(RECTANGLE)=\text{length}* breadth \\ \text{Area}_(RECTANGLE)=l* b \end{gathered}`

By substituting the values, we will have

`\begin{gathered} \text{Area}_(RECTANGLE)=(3n-3)*(n+2) \\ (3n-3)*(n+2)=54 \end{gathered}`

By expanding the brackets, we will have

`\begin{gathered} (3n-3)*(n+2)=54 \\ 3n(n+2)-3(n+2)=54 \\ 3n^2+6n-3n-6=54 \\ 3n^2+3n-6-54=0 \\ 3n^2+3n-60=0 \end{gathered}`

Therefore,

The final answer is = 3n² + 3n - 60 = 0

By factorizing the equation, we will have n^