Question

if ∠a = ∠d = 80°, ab = 16 cm, ac = 24 cm, and de = 8 cm, what is the value of df if △abc ~ △def?
a. 18 cm
b. 14 cm
c. 10 cm
d. 12 cm

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle ABC\sim\triangle DEF\), the ratios of corresponding sides are equal. That is \(\frac{AB}{DE}=\frac{AC}{DF}\).

Step2: Substitute the given values

We know \(AB = 16\mathrm{cm}\), \(AC=24\mathrm{cm}\), and \(DE = 8\mathrm{cm}\). Substituting into \(\frac{AB}{DE}=\frac{AC}{DF}\), we get \(\frac{16}{8}=\frac{24}{DF}\).

Step3: Solve for \(DF\)

Cross - multiply: \(16\times DF=24\times8\). Then \(16DF = 192\). Divide both sides by 16: \(DF=\frac{192}{16}=12\mathrm{cm}\).

Answer:

d. \(12\mathrm{cm}\)