Question

find the value of x that makes \\( \triangle big - \triangle mop \\).
figure is not drawn to scale.

Explanation:

Step1: Use the property of similar triangles

For similar triangles \(\triangle BIG\) and \(\triangle MOP\), the ratios of corresponding sides are equal.
The ratio of \(BG\) to \(MP\) is \(\frac{14}{21}=\frac{2}{3}\). The ratio of \(IG\) to \(OP\) should also be \(\frac{2}{3}\).
We know \(IG = 12\) and \(OP=5x - 2\). So, \(\frac{IG}{OP}=\frac{2}{3}\), which gives \(\frac{12}{5x - 2}=\frac{2}{3}\).

Step2: Cross - multiply

Cross - multiplying the equation \(\frac{12}{5x - 2}=\frac{2}{3}\) gives \(12\times3=2\times(5x - 2)\).

$$36 = 10x-4$$

Step3: Solve for \(x\)

Add \(4\) to both sides of the equation \(36 = 10x-4\):

$$36 + 4=10x$$

$$40 = 10x$$

Divide both sides by \(10\):

$$x = 4$$

Answer:

\(x = 4\)