the perimeter of a square is 75. its length is 2x + 5. find the exact value of the length

To find the length of the square, we use the formula for the perimeter of a square:

\[
P = 4 \times \text{side length}
\]

Given that the perimeter \( P = 75 \) and the side length is expressed as \( 2x + 5 \), we set up the equation:

\[
75 = 4 \times (2x + 5)
\]

Now, let's solve for \( x \):

1. Expand the equation:
   \[
   75 = 4(2x + 5)
   \]
   \[
   75 = 8x + 20
   \]

2. Subtract 20 from both sides:
   \[
   75 - 20 = 8x
   \]
   \[
   55 = 8x
   \]

3. Divide both sides by 8:
   \[
   x = \frac{55}{8}
   \]
   \[
   x = 6.875
   \]

Now, substitute this value of \( x \) back into the expression for the side length:

\[
\text{Side length} = 2x + 5 = 2(6.875) + 5 = 13.75 + 5 = 18.75
\]

Thus, the exact value of the side length is **18.75**.

Would you like any further clarification or additional questions?

Here are 5 related questions:
1. What is the area of the square with this side length?
2. How does the formula for the perimeter of a square compare to the perimeter of a rectangle?
3. How do you find the perimeter of a square when the side length is given algebraically?
4. How would the perimeter change if the side length were expressed as \( 3x + 2 \)?
5. How can you check your solution to ensure the side length is correct?

**Tip**: Always double-check your algebraic steps, especially when dealing with equations that involve distributing terms or simplifying expressions!

The perimeter of a square is 75. Its length is 2x + 5. Find the exact value of the length.

Learn how to find the side length of a square when its perimeter is given as 75 and the side length is expressed algebraically as 2x + 5. This step-by-step solution involves solving linear equations and applying the formula for the perimeter of a square. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation