Question

27) A basketball court is a rectangle with a perimeter of36m^2 + 2m - 10 and a width of m^2. Find an expression for the length.

Answer 1

SOLUTION.

The basketball court is rectangle. To solve this question, we need to know the formula for the perimeter of a rectangle

The perimeter of a rectangle is given by

`\begin{gathered} \text{Perimeter}=2(L+W) \\ \text{Where } \\ L=\text{length and W= Width} \end{gathered}`

The expression giving from the question, we have

`\begin{gathered} \text{perimeter}=36m^2+2m-10 \\ \text{width}=m^2 \end{gathered}`

Substitute into the formula, we have

`\begin{gathered} 36m^2+2m-10=2(L+m^2) \\ \end{gathered}`

factorize the common factor on the lefth-hand side, we have

`\begin{gathered} 2(18m^2+m-5)=2(L+m^2)_{} \\ \text{Divide both sides by 2, we have } \\ 18m^2+m-5=L+m^2 \end{gathered}`

Subtract m² from both sides of the equation, we obtain

`\begin{gathered} 18m^2-m^2+m-5=L+m^2-m^2 \\ \text{Then} \\ 17m^2+m-5=L \end{gathered}`

Hence

The expression for the length is 17m²+ m - 5

Answer: L= 17m²+ m - 5