A rectangular skateboard park has an area of 2 + 15 + 56. What are possible dimensions of the park?

The possible dimensions of the park are (x + 7) and (x + 8) where x is any number

Step-by-step explanation:

If an area of a rectangle is A = ax² + bx + c, then the dimensions of the rectangle are the factors of ax² + bx + c

∵ A rectangular skateboard park has an area of x² + 15x + 56

∴ A = x² + 15x + 56

- Lets factorize the trinomial x² + 15x + 56 into two factors

∵ The last sign of it is (+)

∴ The two factors have the same middle sign

∵ The middle sign of it is (+)

∴ The two factors have (+) as a middle sign

∵ x² = x * x

∵ 56 = 7 * 8

∵ 7 * x + 8 * x = 15x ⇒ middle term

- That means the factors of x² + 15x + 56 are (x + 7) and (x + 8)

∴ The factors of x² + 15x + 56 are (x + 7) and (x + 8)

∵ A = x² + 15x + 56

∴ A = (x + 7) (x + 8)

∵ Area of the rectangle = The product of its dimensions

∴ (x + 7) and (x + 8) are the dimensions of the park

The possible dimensions of the park are (x + 7) and (x + 8) where x is any number