The middle line of the trapezoid is 11 and the smaller base is 5. Find the larger base of the trapezoid.

We denote by x the length of the greater base of this trapezoid.

According to the condition of the problem, the length of the midline of this trapezoid is 11, and the length of the smaller base of this trapezoid is 5.

Using the property of the midline of a trapezoid, namely that in any trapezoid the length of the midline of a trapezoid is equal to half the sum of the lengths of the bases of this trapezoid, we can compose the following equation:

(x + 5) / 2 = 11.

Solving this equation, we get:

x + 5 = 11 * 2;

x + 5 = 22;

x = 22 – 5;

x = 17.

Answer: the length of the larger base of this trapezoid is 17.

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