math
posted by Brigitta .
The longer base of an isosceles trapezium is 20 cm, its legs are 10cm. The legs of the trapezium are extended by 8 cm long to gain an isosceles triangle.Find the shorter base of the trapezium. Please help me:)

did you make a sketch?
I have a large isosceles triangle containing your original trapezium
The sides of the triangle are made up of the segments 10 and 8 for a total length of 18 each
I see a smaller isosceles triangle contained and similar to a larger isosceles triangle
let the smaller base be x
remember the sides of similar triangles are in the same ratio
so....
x/8 = 20/18
x = 8(20/18) = 80/9 or appr. 8.89 cm 
thank u so much!:)