The middle line of the trapezoid is 41 and the smaller base is 20. Find the larger base of the trapezoid.

The middle line of the trapezoid is equal to the half-sum of its bases, from there: m = (a + b) / 2, where a is a larger base, b is a smaller base. According to the condition, m = 41, b = 20. Substitute the data on the value condition in the formula and find the length of the larger base of the trapezoid: (a + 20) / 2 = 41. We use the main property of the “cross to cross” proportion (to find the unknown numerator of the first fraction , it is necessary to multiply the denominator of the first fraction by the numerator of the second fraction and divide by the denominator of the second fraction, the number 41 can be represented as a fraction with the denominator 1): a + 20 = 2 * 41; a + 20 = 82; a = 82 – 20; a = 62.
Answer: a = 62.