Question

From the below figure the value of x= _____.

• A. 11
• B. 12.83
• C. 14
• D. 25

Answer 1

The Correct Option is A

To solve the problem, we need to find the value of $x$ using the properties of triangles and trigonometry.

1. Observing the Triangle Configuration:
In the given figure, triangles $\triangle ABC$ and $\triangle DEC$ share angle $\angle C$, and angles $\angle A = \angle E$ (both marked as equal), which means the triangles are similar by AA similarity.

2. Using Property of Similar Triangles:
From similar triangles $\triangle ABC \sim \triangle DEC$, the corresponding sides are in proportion:

$\frac{AB}{DE} = \frac{AC}{DC}$

3. Substituting Given Values:

$AB = 24$

$DE = 12$

$BC = 22$

Let $x = DC$

Using similar triangles, we write:

$\frac{24}{12} = \frac{22}{x}$

4. Solving the Proportion:

$\frac{24}{12} = 2$, so:

$2 = \frac{22}{x}$

$x = \frac{22}{2} = 11$

Final Answer:
The value of $x$ is $ \mathbf{11} $.