Question

The total area of the large rectangle is 24m2. Determine the value of x​

Answer 1

Answer:

x = 2  

Step-by-step explanation:

1. Calculate the sum of the areas of the smaller rectangles.

$\begin{array}{rcl}\text{A} & = & 2x \\\text{B} & = & x^{2} \\\text{C} & = & x^{2} \\\text{D} & = & 4 \\\text{E} & = & 2x \\\text{F} & = & 2x \\\text{Total} & = & 2x^{2} + 6x + 4 = 24\\\end{array}$

2. Factor the quadratic

$\begin{array}{rcl}2x^{2} + 6x + 4 & = & 24\\x^{2} + 3x + 2 & = & 12\\x^{2} + 3x - 10 & = & 0\\(x + 5)(x - 2) & = & 0\\\end{array}$

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

$\begin{array}{rcr}\text{A} & = & 4 \\\text{B} & = & 4 \\\text{C} & = & 4 \\\text{D} & = & 4 \\\text{E} & = & 4 \\\text{F} & = & 4 \\\text{Total} & = &24\\\end{array}$

OK.