Question

1. if bc = 5.3, cd = 8.8, and ad = 14.3, find ab to the nearest tenth.

1.6
3.3
23.7
8.6

Explanation:

Step1: Assume similarity of triangles

Assume \(\triangle ABC\sim\triangle ADC\) (by AA - Angle - Angle similarity if the angles \(\angle BAC=\angle CAD\) and \(\angle ABC=\angle ADC\)). Then the ratios of corresponding sides are equal, i.e., \(\frac{AB}{AD}=\frac{BC}{CD}\).

Step2: Rearrange the formula to solve for \(AB\)

We can rewrite the proportion \(\frac{AB}{AD}=\frac{BC}{CD}\) as \(AB=\frac{BC\times AD}{CD}\).

Step3: Substitute the given values

Given \(BC = 5.3\), \(CD=8.8\), and \(AD = 14.3\). Substitute these values into the formula: \(AB=\frac{5.3\times14.3}{8.8}\).
First, calculate \(5.3\times14.3 = 75.79\). Then, \(\frac{75.79}{8.8}\approx8.6\).

Answer:

8.6