Question

the total area of the figure to the right is 459 cm². use this fact to write an equation involving x. then solve the equation to find the value of x
the equation is
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Explanation:

Step1: Split figure into 3 rectangles

We can divide the shape into:

1. A large vertical rectangle on the left: dimensions $x$ and $(20 + x)$
2. A small horizontal rectangle on the bottom right: dimensions $(10 - x)$ and $x$
3. A top right rectangle: dimensions $10$ and $(20 - x)$

Step2: Calculate total area

Sum the areas of the three rectangles, set equal to 459:

$$ x(20+x) + x(10-x) + 10(20-x) = 459 $$

Step3: Expand each term

$$ 20x + x^2 + 10x - x^2 + 200 - 10x = 459 $$

Step4: Simplify the equation

Combine like terms:

$$ (20x+10x-10x) + (x^2 - x^2) + 200 = 459 \\ 20x + 200 = 459 $$

Step5: Isolate the variable term

Subtract 200 from both sides:

$$ 20x = 459 - 200 \\ 20x = 259 $$

Step6: Solve for x

Divide both sides by 20:

$$ x = \frac{259}{20} $$

Answer:

The equation is $20x + 200 = 459$ (or the expanded form $x(20+x) + x(10-x) + 10(20-x) = 459$), and $x = 12.95$ cm