Question

lake quiz exit = ge question 9 2 pts △abc ~△qrs c = 21.7; s = 11.3; q = 6; b = 12 what is a? hint: draw it with the values. round answers to two decimal places (the nearest hundredth).

Explanation:

Step1: Recall Similar Triangles Ratio

For similar triangles \( \triangle ABC \sim \triangle QRS \), the ratios of corresponding sides are equal. So, \( \frac{a}{q}=\frac{b}{r}=\frac{c}{s} \). We can use \( \frac{a}{q}=\frac{c}{s} \) (or \( \frac{a}{q}=\frac{b}{r} \), but let's use \( \frac{a}{q}=\frac{c}{s} \) with given values).

Step2: Substitute Values into Proportion

We know \( c = 21.7 \), \( s = 11.3 \), \( q = 6 \). The proportion is \( \frac{a}{6}=\frac{21.7}{11.3} \).

Step3: Solve for \( a \)

Multiply both sides by 6: \( a=\frac{21.7\times6}{11.3} \). Calculate numerator: \( 21.7\times6 = 130.2 \). Then divide by 11.3: \( a=\frac{130.2}{11.3}\approx11.52 \).

Answer:

\( 11.52 \)