A construction engineer is designing a square foundation where the area is defined by the expression ${}49x^2 + 84xy + 36y^2$. To find the side length, the engineer needs to recognize the factored form of this area expression as a squared binomial. Which of the following is the correct factored form?

A quality assurance inspector is verifying the area of a square machine component, which is modeled by the expression ${}49x^2 + 84xy + 36y^2$. When factoring this area to find the side length, the inspector identifies the base values as ${}7x$ and ${}6y$. True or False: To confirm this expression represents a perfect square, the inspector must recall that the middle term ${}84xy$ should be exactly twice the product of ${}7x$ and ${}6y$.

An urban planner is designing a square park with an area represented by the expression ${}49x^2 + 84xy + 36y^2$. To determine the fencing requirements, the planner identifies the dimensions using the perfect square trinomial pattern $a^2 + 2ab + b^2 = (a + b)^2$. Match each role in the algebraic pattern to its corresponding component from the park's area expression.

A logistics coordinator is verifying the side length of a square storage container with an area represented by the trinomial ${}49x^2 + 84xy + 36y^2$. To find the side length using the perfect square trinomial pattern, arrange the following steps in the correct logical order.

A packaging engineer is designing a square shipping box with a base area of ${}49x^2 + 84xy + 36y^2$ square inches. To determine the dimensions for the box's footprint, the engineer must identify the side length. According to the perfect square trinomial pattern, the binomial that represents the side length of the box is ____.