Question

question 10 of 25
in the diagram below, △abc ~ △dec. what is the value of x?
a. 4
b. 5
c. 3
d. 6

Explanation:

Step1: Set up proportion for similar triangles

Since $\triangle ABC\sim\triangle DEC$, the ratios of corresponding sides are equal. So, $\frac{BC}{EC}=\frac{AC}{DC}$, which gives $\frac{21}{7}=\frac{24 - x}{x}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{21}{7}=\frac{24 - x}{x}$ gives $21x=7(24 - x)$.

Step3: Expand the right - hand side

Expanding $7(24 - x)$ gives $21x = 168-7x$.

Step4: Add $7x$ to both sides

Adding $7x$ to both sides: $21x+7x=168-7x + 7x$, resulting in $28x=168$.

Step5: Solve for $x$

Dividing both sides by 28: $x=\frac{168}{28}=6$.

Answer:

D. 6