Question

ALGEBRAIC PROOF!!!! PLS HELP!!! The area of a rectangular blanket is 20 square feet. The blanket's length is (2x + 1) ft and the blanket's width is 2x ft. find the dimensions of the blanket. provide justification for each step.

Answer 1

Answer:

Length: 5 ft; width: 4 ft.

Step-by-step explanation:

A = LW     formula for area of rectangle

(2x + 1)(2x) = 20      substitute length, width, and area into formula

4x² + 2x - 20 = 0      use the distributive property to multiply out left side

2x² + x - 10 = 0         divide both sides of equation by 2

(2x + 5)(x - 2) = 0        factor out trinomial

2x + 5 = 0  or  x - 2 = 0        use zero product rule to solve for x

2x = -5  or x = 2       subtract 5 from both sides; add 2 to both sides

x = -5/2  or  x = 2

We discard x = -5/2 since it would give negative length and width, and the length and width cannot be negative.

Length: 2x + 1 = 2(2) + 1 = 5

Width: 2x = 2(2) = 4

Length: 5 ft; width: 4 ft.