Question

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

Answer 1

x = 2

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.