Math Problem Statement

the length of a garden is 11 more than its width. if the perimeter is 90, what is the measure of its width?

Solution

Let the width of the garden be represented by ww. According to the problem, the length of the garden is 11 more than the width, so the length is w+11w + 11.

The formula for the perimeter of a rectangle is:

P=2×(Length+Width)P = 2 \times (\text{Length} + \text{Width})

We are told that the perimeter is 90, so we can substitute the values into the formula:

90=2×((w+11)+w)90 = 2 \times ((w + 11) + w)

Simplify the equation:

90=2×(2w+11)90 = 2 \times (2w + 11)

Next, divide both sides by 2:

45=2w+1145 = 2w + 11

Now, subtract 11 from both sides:

34=2w34 = 2w

Finally, divide both sides by 2:

w=17w = 17

So, the width of the garden is 1717 units.

Do you want any more details or have additional questions on this topic?

Here are 5 related questions:

  1. How do we calculate the area of the garden?
  2. What would the perimeter be if the length were 20 more than the width?
  3. What happens if the perimeter were reduced by 10 units?
  4. How would we solve this if the length were half the width instead of 11 more?
  5. How does changing the dimensions affect the perimeter of the garden?

Tip: Double-check your perimeter formula, especially when variables change like this!

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Math Problem Analysis

Mathematical Concepts

Algebra
Perimeter of a Rectangle

Formulas

Perimeter of a rectangle: P = 2 × (Length + Width)

Theorems

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Suitable Grade Level

Grades 7-9