Question

in the figure below, ( ad=(3x - 14)\text{ cm} ). find the value of ( x ).

Explanation:

Step1: Identify congruent triangles

From the figure, we can see that $\triangle BAD$ and $\triangle BCD$ are congruent (by AAS or ASA, since they have a right angle, a $36^\circ$ angle, and share the side $BD$). So, the corresponding sides $AD$ and $CD$ should be equal.

Step2: Set up the equation

We know that $CD = 13$ cm and $AD=(3x - 14)$ cm. Since $AD = CD$, we set up the equation:
$$3x-14 = 13$$

Step3: Solve for $x$

Add 14 to both sides of the equation:
$$3x=13 + 14$$
$$3x=27$$
Divide both sides by 3:
$$x=\frac{27}{3}$$
$$x = 9$$

Answer:

The value of $x$ is $\boldsymbol{9}$.