# Chapter 7 - Section 7.6 - Proportions and Problem Solving with Rational Equations - Exercise Set: 74

$y= 3.5$ units

#### Work Step by Step

Step 1: Since the triangles are similar, their corresponding sides are in proportion. Step 2: This means that $\frac{7}{14}=\frac{5}{10}=\frac{y}{7}$. Step 3: Since the corresponding sides are in proportion, we can take any set of known sides and equate it to the set of sides containing the unknown. Step 4: Therefore, $\frac{5}{10}=\frac{y}{7}$. Step 5: Solving through cross multiplication: $10y=5\times7$. Step 6: $10y=35$. Step 7: $y= 3.5$ units. Check: Step 1: Equating the three proportions to see if they reduce to the same fraction: $\frac{7}{14}=\frac{5}{10}=\frac{3.5}{7}$. Step 2: $\frac{1}{2}=\frac{1}{2}=\frac{1}{2}$. Step 3: Therefore, the answer is accurate.

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