Question

The width of a small rectangular playground is 3 meters less than the length ofthe playground.If the area of the playground_5,1 square meters, what are the dimensions ofthe playground? State the units of the dimensiops. Make sure you reject the answer thatcannot be a solution.You MUST solve this problem using a quadratic equation. Draw a diagram that representsthe problem.

Answer 1

Taking l and w as the length and the width of the rectangle respectively, we have that:

`w=l-3`

We know that the area of a rectangle is:

`A=w\cdot l`

Replace A for the given value of the area and w for the expression stated:

`54=(l-3)\cdot l`

Solve the operations and write the equation as a quadratic expression:

`\begin{gathered} 54=l^2-3l \\ 0=l^2-3l-54 \end{gathered}`

Solve the quadratic equation using factorization:

`\begin{gathered} 0=(l-9)(l+6) \\ l-9=0 \\ l=9 \\ l+6=0 \\ l=-6 \end{gathered}`

For this context, the value of l that we can use is 9. It means that the length of the triangle is 9m.

Use this value and the first expression to find w:

`\begin{gathered} w=l-3 \\ w=9-3 \\ w=6 \end{gathered}`

The width of the triangle is 6m.