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This problem trains for: SAT-I, AMC-8, GMAT.

A trapezoid with bases of lengths: 12 and 26 units has non-parallel sides of lengths 8.5 and 12.5 units. What is the ratio between the area of the smallest rectangle in which this trapezoid can be inscribed and that of the largest rectangle that can be inscribed in this trapezoid?

This is another one of those problems in which the examiner provides too much data in order to make the student compute and waste time.

Denote the height of the trapezoid with h and do not bother to find its length.

Let's look at the largest rectangle that can be inscribed in the trapezoid.

figure

Its area is:

equation

Let's look at the smallest rectangle that the trapezoid can be inscribed in.

figure

Its area is:

equation

Their ratio is:

equation