Suppose given an isosceles triangle with a leg measuring 5 in. two lines are drawn through some point on the base, each parallel to one of the legs. find the perimeter of the constructed parallelogram.

We have an isosceles triangle  and 2 lines that are drawn through some ( any ) point on the base. The both lines are parallel to one of the legs. Then those lines with the legs of the triangle make a parallelogram. We can say that x and y are the sides of the parallelogram. Then: x + y = 5 in. And the perimeter of the parallelogram: P = 2 x + 2 y = 2 * ( x + y ).
P = 2 * 5 = 10 in.  The rest is in the attachment.
The perimeter of the constructed parallelogram is 10 inches.