# Help Zone

### Student Question

Secondary II • 2yr.

Hello, can you help me with this question please? :

The length of a rectangular park is 5 m more than three times the width. The park is surrounded by a sidewalk, 3 m wide, with the sidewalk increasing the area of ​​the park by 1986 m ^ 2.

What is the area of ​​the park without the sidewalk?

Mathematics

## Explanations (1)

• Explanation from Alloprof

Explanation from Alloprof

This Explanation was submitted by a member of the Alloprof team.

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Team Alloprof • 2yr.

Hello!

In this question, it is important to translate the situation into an equation. Just follow these steps:

• Carefully read the written problem and identify the known data and variables. Thus, in your situation, you can set the variables of the length and the width of the park, using a variable (x, y, z or other)!
• Identify the relationship between the variables. Subsequently, I strongly advise you to draw a picture of the situation, because it is important to clearly visualize the measurements. In this case, the area of ​​the park, a rectangle (bxh) added to 1986 m ^ 2 is equal to the area of ​​the park with the sidewalk.
• Translate this relation by an equation or by an algebraic expression. So, thanks to your drawing, you are able to find the relation between the variables. (! Pssssst The equation should look like this: the park area with sidewalk = area of the park + 1986 m ^ 2 You only have to replace the two areas with the variables found in the first step..)

Finally, you just have to isolate the variable to find the dimensions of the park. It will eventually be necessary to calculate the new area.

I hope this has enlightened you! Do not hesitate if you have any other questions, it will be a pleasure to help you!

You can also visit our Alloprof page on the subject for examples of translating situations into equations.