Question

The perimeter of a rectangular field is 354m.

If the width of the field is 81m , what is its length?

Answer 1

The length of the field is equal to 96 m.

General Formulas and Concepts:
Algebra I

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Terms/Coefficients

Geometry

Perimeter Formula [Rectangle]: P = 2l + 2w

• l is length
• w is width

Explanation:

Step 1: Define

Identify given.

P = 354 m

w = 81 m

Step 2: Find Length

1. [Perimeter Formula - Rectangle] Substitute in variables:
   354 m = 2l + 2(81 m)
2. Simplify:
   354 m = 2l + 162 m
3. [Subtraction Property of Equality] Isolate l term:
   192 m = 2l
4. [Division Property of Equality] Isolate l:
   96 m = l
5. Rewrite:
   l = 96 m

∴ we have found the length of the field to be 96 meters.

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Topic: Geometry