Question

given that the pair of triangles is similar, find the missing length. 5) solve. 6) two times the reciprocal of a number equals 48 times the reciprocal of 60. find the number.

Explanation:

Step1: Set up proportion for similar triangles

For similar triangles, the ratios of corresponding sides are equal. So, $\frac{x}{7}=\frac{48}{24}$.

Step2: Solve the proportion for $x$

Cross - multiply gives $24x = 48\times7$. Then $x=\frac{48\times7}{24}$. Calculate $48\times7 = 336$, and $\frac{336}{24}=14$.

Step3: Solve the reciprocal problem

Let the number be $n$. The equation is $2\times\frac{1}{n}=48\times\frac{1}{60}$. Cross - multiply: $2\times60 = 48n$. So, $120 = 48n$. Then $n=\frac{120}{48}=\frac{5}{2}=2.5$.

Answer:

$x = 14$
The number is $2.5$