Question

marnie solved the proportion \\(\frac{150}{170} = \frac{x}{510}\\) to find the value of ( x ) in the enlarged parallelogram. image of two parallelograms: small with 150 cm and 170 cm, large with ( x ) cm and 510 cm, labeled
ot drawn to scale\ what is the value of ( x )? \\( \circ \\ x = 266 \\) \\( \circ \\ x = 300 \\) \\( \circ \\ x = 340 \\) \\( \circ \\ x = 450 \\)

Explanation:

Step1: Cross - multiply the proportion

Given the proportion \(\frac{150}{170}=\frac{x}{510}\), cross - multiplying gives us \(170x = 150\times510\).

Step2: Calculate the right - hand side

First, calculate \(150\times510\). \(150\times510 = 150\times(500 + 10)=150\times500+150\times10 = 75000+1500 = 76500\). So the equation becomes \(170x=76500\).

Step3: Solve for \(x\)

To solve for \(x\), divide both sides of the equation by 170. \(x=\frac{76500}{170}\). Simplifying, we can divide numerator and denominator by 10 first to get \(\frac{7650}{17}\). Then, \(7650\div17 = 450\).

Answer:

\( x = 450 \)