Math Problem Statement

the length of a triangle is R cm the with it is 5 cm shorter than the length write and simplify an expression for the perimeter of the rectangle

Solution

To express the perimeter of a rectangle with length RR cm and width R5R - 5 cm (since the width is 5 cm shorter than the length), we can follow these steps:

Formula for the perimeter of a rectangle:

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

Substituting the values:

Perimeter=2×(R+(R5))\text{Perimeter} = 2 \times (R + (R - 5))

Simplifying:

Perimeter=2×(R+R5)\text{Perimeter} = 2 \times (R + R - 5) Perimeter=2×(2R5)\text{Perimeter} = 2 \times (2R - 5) Perimeter=4R10\text{Perimeter} = 4R - 10

So, the simplified expression for the perimeter of the rectangle is 4R104R - 10 cm.

Would you like further details on this?

Here are some related questions to consider:

  1. How would the expression change if the width were 5 cm longer than the length?
  2. What is the perimeter if R=8R = 8 cm?
  3. How do you calculate the area of this rectangle?
  4. What if both the length and width were decreased by 2 cm?
  5. How would the perimeter change if both the length and width were doubled?

Tip: Always double-check if a problem asks for simplification or specific values before finalizing your answer.

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Math Problem Analysis

Mathematical Concepts

Algebra
Geometry
Perimeter Calculation

Formulas

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

Theorems

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Suitable Grade Level

Grades 6-8