find the value of x in the isosceles triangle shown below.

Explanation:

Step1: Use the property of similar - triangles

Let's assume the two isosceles triangles are similar. If we consider the ratios of corresponding sides.

Step2: Set up the proportion

Let the larger isosceles triangle have sides (8,8,4) and the smaller one have sides (x,x,5). Since the triangles are similar, the ratio of the non - equal sides is equal to the ratio of the equal sides. So, (\frac{4}{5}=\frac{8}{x}).

Step3: Cross - multiply and solve for (x)

Cross - multiplying gives us (4x = 8\times5), which simplifies to (4x=40). Then, dividing both sides by 4, we get (x = 10).

Answer:

10