Question

what is the value of x, the width, and height of the wall? round your answer to the nearest hundredth.
a wall has paneling made up of rectangles, with an area of 30 square feet each, as shown. there are four rectangles along the height and three along the top. the edge of each rectangle in the paneling is (2x + 3) feet in width and (4x + 2) feet in height.
values: 5, 9, 3, -3, 10, 12, 24, 1, -6, :

Explanation:

Step1: Set total area equation

Total area = 4 × area of one rectangle
$$30 = 4\times(2x+3)(4x+2)$$

Step2: Simplify the equation

Divide both sides by 4, expand right side:
$$\frac{30}{4} = (2x+3)(4x+2)$$
$$7.5 = 8x^2 + 4x + 12x + 6$$
$$8x^2 + 16x - 1.5 = 0$$

Step3: Solve quadratic equation

Use quadratic formula $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$, where $a=8$, $b=16$, $c=-1.5$:
$$x=\frac{-16\pm\sqrt{16^2-4\times8\times(-1.5)}}{2\times8}$$
$$x=\frac{-16\pm\sqrt{256+48}}{16}$$
$$x=\frac{-16\pm\sqrt{304}}{16}$$
$$x=\frac{-16\pm17.4356}{16}$$
Take positive root (length can't be negative):
$$x=\frac{1.4356}{16}\approx0.09$$

Step4: Calculate height of wall

Height = $3\times(4x+2)$
$$\text{Height}=3\times(4\times0.09+2)=3\times(0.36+2)=3\times2.36=7.08$$

Step5: Calculate width of wall

Width = $2x+3$
$$\text{Width}=2\times0.09+3=0.18+3=3.18$$

Answer:

Value of x	Height	Width