Math Problem Statement

The perimeter of a rectangle whose length exceeds the width. w by 5.

Solution

Let's denote the width of the rectangle as ww and the length as ll. According to the problem, the length exceeds the width by 5 units. Therefore, we can write:

l=w+5l = w + 5

The formula for the perimeter PP of a rectangle is:

P=2l+2wP = 2l + 2w

Substitute l=w+5l = w + 5 into the perimeter formula:

P=2(w+5)+2wP = 2(w + 5) + 2w

Now, simplify:

P=2w+10+2w=4w+10P = 2w + 10 + 2w = 4w + 10

So, the perimeter of the rectangle is:

P=4w+10P = 4w + 10

Do you need further details or explanations on this?

Here are 5 related questions for further practice:

  1. If the width ww is 7 units, what is the perimeter of the rectangle?
  2. If the perimeter is 50 units, what is the width of the rectangle?
  3. How does the formula for perimeter change if the length exceeds the width by 7 units instead of 5?
  4. If the width ww is doubled, how does that affect the perimeter?
  5. How would you calculate the area of this rectangle?

Tip: When working with formulas, always substitute known values carefully to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Geometry
Algebra

Formulas

Perimeter of a rectangle: P = 2l + 2w
Length and width relationship: l = w + 5

Theorems

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Suitable Grade Level

Grades 6-8