The similar triangle is the image of the bigger triangle after a sequence of transformations. what is the value of x?

The value of x is:  2.5 units

Two triangles are said to be similar if the ratio of the corresponding sides of the two triangles are equal.

i.e. if two triangles ΔABC and ΔDEF are similar such that the sides of the triangle ABC are a, b and c and the corresponding sides in ΔDEF are d,e and f respectively then we have:

Here we have the base length of the orange i.e. the quadrant above the x-axis as: 8 units

and the base length of the similar triangle i.e. triangle below x-axis as:  4 units.

i.e. we have: a=8 and d=4

and  b=5 and e=x

Hence, we have:

i.e.

Hence, we have:

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step-by-step explanation: