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The painting shown at the right has an area of
360in^(2). What is the value of
x ?

The painting shown at the right has an area of $360 \mathrm{in}^{2}$ . What is the value of $x$ ?

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Which word problem matches the one-step equation?

Full solution

Q. The painting shown at the right has an area of

360 \mathrm{in}^{2}

. What is the value of

x

?

Assume Rectangle Dimensions: Assume the painting is a rectangle with length $x$ inches and width $(x - 6)$ inches. The area of a rectangle is length times width. $\newline$ Calculation: Area = $x \times (x - 6)$ $\newline$ Set the area equal to $360$ square inches: $x \times (x - 6) = 360$
Calculate Area: Distribute $x$ across $(x - 6)$ : $x^2 - 6x = 360$
Distribute $x$ : Subtract $360$ from both sides to set the equation to zero: $x^2 - 6x - 360 = 0$
Subtract $360$ : Factor the quadratic equation: (x - \(24)(x + $15$ ) = $0$ \
Factor Quadratic Equation: Set each factor equal to zero and solve for $x$ : $x - 24 = 0$ or $x + 15 = 0$
Solve for x: Solve the first equation: $x = 24$ Solve the second equation: $x = -15$
Check Validity: Since a painting can't have a negative length, $x = -15$ is not a valid solution.

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