Question

lesson 9: side length quotients in similar triangles cool down: similar sides the 2 triangles shown are similar. find the side proportions of a and b for the larger triangle.

Explanation:

Step1: Use the property of similar triangles

Since the two triangles are similar, the ratios of their corresponding sides are equal. For the smaller triangle, the ratio of the sides is \(\frac{1.4}{2.1}\). For the larger triangle, the ratio of the corresponding sides is \(\frac{2.1}{a}\) and \(\frac{1.4}{b}\).
First, simplify \(\frac{1.4}{2.1}=\frac{14}{21}=\frac{2}{3}\).

Step2: Find side \(a\)

We know that \(\frac{1.4}{2.1}=\frac{2.1}{a}\). Cross - multiply: \(1.4a = 2.1\times2.1\). Then \(a=\frac{2.1\times2.1}{1.4}=\frac{4.41}{1.4}=3.15\).

Step3: Find side \(b\)

We know that \(\frac{1.4}{2.1}=\frac{1.4}{b}\). Cross - multiply: \(1.4b = 1.4\times2.1\). Then \(b = 2.1\times\frac{1.4}{1.4}=2.1\times1 = 3.5\).

Answer:

\(a = 3.15\) and \(b = 3.5\)