You are managing materials for a new office layout. The area of a large square modular tile is given by the algebraic expression ${}4x^2 + 12x + 9$. To determine the formula for the length of one side of the tile, you must recall the perfect square trinomial pattern to factor the area. Which of the following is the correctly factored form?

You are a logistics coordinator designing a square-shaped safety zone in a production plant. The total area required is given by the expression ${}4x^2 + 12x + 9$. To determine the specific side length for construction, arrange the following steps in the correct order to factor this expression using the square of a binomial pattern.

In a construction project, a carpenter is verifying the dimensions of a square wooden deck. If the area of the deck is represented by the expression ${}4x^2 + 12x + 9$, then according to the perfect square trinomial pattern, the binomial representing the length of one side of the deck is ${}2x + 3$.

An architect is designing a square-shaped lobby with a floor area represented by the expression ${}4x^2 + 12x + 9$. To determine the dimensions for construction, the architect uses the perfect square trinomial pattern $a^2 + 2ab + b^2 = (a + b)^2$. Match each component of the factoring process to its corresponding value for this specific lobby area.

A construction foreman is verifying the dimensions of a square concrete slab. The area of the slab is recorded in the blueprints as ${}4x^2 + 12x + 9$ square feet. To find the length of one side of the slab, the foreman factors this expression using the perfect square trinomial pattern. The binomial representing the side length of the square slab is ____.