Question

given that △abc~△def, solve for x.
a 24 c d x f
a. 2
b. 3
c. 6
d. 4

Explanation:

Step1: Set up proportion

Since $\triangle ABC\sim\triangle DEF$, the ratios of corresponding sides are equal. So, $\frac{AC}{DF}=\frac{BC}{EF}$. Substituting the given values, we get $\frac{24}{x}=\frac{42}{7}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{24}{x}=\frac{42}{7}$ gives us $42x = 24\times7$.

Step3: Solve for x

First, calculate $24\times7 = 168$. Then, we have $42x=168$. Divide both sides by 42: $x=\frac{168}{42}=4$.

Answer:

D. 4