The area of a rectangular classroom is x² - 25. Which of the following binomials could represent the length and the width of the room?

Question: The area of a rectangular classroom is x² - 25. Which of the following binomials could represent the length and the width of the room?

Solution:
We know that the area of a rectangle = length × width.
Given area = x² - 25.
We can factorize this expression using the algebraic identity for the difference of two squares:
a² - b² = (a + b)(a - b)

Now,
x² - 25
⇒ x² - 5²
⇒ (x + 5)(x - 5)

So, the binomials representing the length and the width are (x + 5) and (x - 5).
∴ The correct option is (x + 5)(x - 5).