Answer:
x = 2
Step-by-step explanation:
1. Calculate the sum of the areas of the smaller rectangles.
[tex]\begin{array}{rcl}\text{A} & = & 2x \\\text{B} & = & x^{2} \\\text{C} & = & x^{2} \\\text{D} & = & 4 \\\text{E} & = & 2x \\\text{F} & = & 2x \\\text{Total} & = & 2x^{2} + 6x + 4 = 24\\\end{array}[/tex]
2. Factor the quadratic
[tex]\begin{array}{rcl}2x^{2} + 6x + 4 & = & 24\\x^{2} + 3x + 2 & = & 12\\x^{2} + 3x - 10 & = & 0\\(x + 5)(x - 2) & = & 0\\\end{array}[/tex]
3. Solve the quadratic
(x + 5)(x - 2) = 0
Apply the zero-product rule
x + 5 = 0 x - 2 = 0
x = -5 x = 2
We reject the negative value because we can't have a negative length.
Therefore, x = 2.
4. Check the areas
[tex]\begin{array}{rcr}\text{A} & = & 4 \\\text{B} & = & 4 \\\text{C} & = & 4 \\\text{D} & = & 4 \\\text{E} & = & 4 \\\text{F} & = & 4 \\\text{Total} & = &24\\\end{array}[/tex]
OK.
