the area of a rectangular swimming pool is given by 4x^2+9x+2ft^2.One side length of the pool by 4x+1feet. What is an algebraic expression for the other side lengeth of the pool and simplify and include correct units as a part oy your answer. please help
length = (4x^2 + 9x + 2)/(4x+1)
= (4x+1)(x+2)/(4x+1) = x+2
To find the algebraic expression for the other side length of the rectangular swimming pool, we'll use the area formula of a rectangle, which states that:
Area = Length × Width
Given that the area of the pool is 4x^2 + 9x + 2 ft^2 and one side length is 4x + 1 feet, we can write the equation as:
(4x + 1) × Width = 4x^2 + 9x + 2
Now, let's solve for the width (the other side length) algebraically:
Expand the left side of the equation by using the distributive property:
4x * Width + 1 * Width = 4x^2 + 9x + 2
Simplify:
4x * Width + Width = 4x^2 + 9x + 2
Combine like terms:
(4x + 1) * Width = 4x^2 + 9x + 2
Divide both sides of the equation by (4x + 1) to isolate "Width":
Width = (4x^2 + 9x + 2) / (4x + 1)
Therefore, the algebraic expression for the other side length of the rectangular swimming pool is (4x^2 + 9x + 2) / (4x + 1) feet.