In trapeziums ABCD, BC || AD, MP is the middle line of the trapezoid. Find the base of the trapezoids

univerkov | May 5, 2021 | education

In trapeziums ABCD, BC || AD, MP is the middle line of the trapezoid. Find the base of the trapezoids if one of them is 3 cm less than the other, and the middle line is 9 cm.

Let the length of the smaller base be equal to X cm, BC = X cm, then, by condition, the larger base will be: AD = (X + 3) cm.

Let’s use the formula for the length of the midline of a trapezoid.

KR = (BC + AD) / 2 = (X + X + 3) / 2 = 9 cm.

2 * X + 3 = 18.

X = BC = 15/2 = 7.5 cm.

Then AD = 7.5 + 3 = 10.5 cm.

Answer: The bases of the trapezoid are 7.5 cm and 10.5 cm.

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