Question

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