The middle line of the trapezoid is 18. One base of the trapezoid is half the size of the other

The middle line of the trapezoid is 18. One base of the trapezoid is half the size of the other. Find the larger base of the trapezoid.

Given: trapezoid, l is the middle line of the trapezoid, l = 18; a – larger base of the trapezoid; b – smaller base of the trapezoid; b is 2 times less than a.

Find: the larger base of the trapezoid a.

Solution:

1 way. b is 2 times less than a, which means that a = 2 * b.

The middle line of the trapezoid is parallel to the bases and equal to their half-sum.

l = (a + b): 2; l = (2 * b + b): 2; l = 3 * b: 2;

b = 2 * l: 3; b = 2 * 18: 3; b = 12;

a = 2 * b = 2 * 12 = 24.

Method 2. b = 0.5 * a, then l = (a + 0.5 * a): 2; l = 1.5 * a: 2;

a = 2 * l: 1.5; a = 2 * 18: 1.5 = 24.

Answer: 24 is the larger base of the trapezoid.