Question

question 10
△ abc ~△ qrs
c = 37.8; s = 14.8; q = 9; b = 19
what is r?
hint: draw it with the values.
round answers to two decimal places (the nearest hundredth).

Explanation:

Step1: Recall Similar Triangles Property

Since \(\triangle ABC \sim \triangle QRS\), the corresponding sides are proportional. So, \(\frac{c}{s}=\frac{b}{r}\).

Step2: Substitute Known Values

We know \(c = 37.8\), \(s = 14.8\), \(b = 19\), and we need to find \(r\). Substituting into the proportion: \(\frac{37.8}{14.8}=\frac{19}{r}\).

Step3: Cross - Multiply to Solve for \(r\)

Cross - multiplying gives \(37.8\times r=14.8\times19\). First, calculate \(14.8\times19 = 281.2\). Then, \(r=\frac{281.2}{37.8}\).

Step4: Calculate the Value of \(r\)

\(r=\frac{281.2}{37.8}\approx7.44\) (rounded to two decimal places).

Answer:

\(7.44\)