Question

algebra the length (in inches) of two sides of a regular pentagon are represented by the expressions $5x - 27$ and $2x - 6$. find the length of a side of the pentagon.

length of a side of the pentagon = \boxed{\space} inches

Explanation:

Step1: Set the expressions equal (regular pentagon sides are equal)

Since a regular pentagon has all sides equal, we set \(5x - 27=2x - 6\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides: \(5x - 2x-27 = 2x - 2x-6\), which simplifies to \(3x - 27=-6\).
Then add 27 to both sides: \(3x - 27 + 27=-6 + 27\), so \(3x = 21\).
Divide both sides by 3: \(x=\frac{21}{3}=7\).

Step3: Find the side length

Substitute \(x = 7\) into one of the expressions, say \(2x - 6\).
\(2(7)-6 = 14 - 6 = 8\). (We could also use \(5x - 27\): \(5(7)-27 = 35 - 27 = 8\), same result.)

Answer:

8