Question

A quadrilaterals smallest side measures 29 mm and its largest side measures 38 mm. A similar quadrilaterals largest side measures 95 mm. What is the measure of its smallest side?

Answer 1

Let $x$ be the length of the smallest side of the similar quadrilateral. Since the ratio of corresponding side lengths between similar quadrilaterals is the same, we set up the proportion $\dfrac{29}{x} = \dfrac{95}{38}$. Cross-multiplying yields $29\cdot 38 = 95x \Rightarrow x = \dfrac{29\cdot 38}{95} = \dfrac{(29\cdot 5)(2\cdot 19)}{5\cdot 19} = \boxed{58 \text{ mm}}$.