The middle line of the trapezoid is 18. Find its base if one of them is: a) 2 times larger than the other

| January 28, 2021 | education

The middle line of the trapezoid is 18. Find its base if one of them is: a) 2 times larger than the other. b) 3 times less than the other.

and)

Let the length of the smaller base of the trapezoid be equal to X cm, then the length of the larger base, by condition, is equal to 2 * X cm.

The length of the midline of the trapezoid is equal to half the sum of the lengths of its bases.

Then 18 = (X + 2 * X) / 2.

3 * X = 6.

X = 36/3 = 12.

The length of the smaller base is 12 cm.

The length of the larger base is 2 * 12 = 24 cm.

Answer: The bases of the trapezoid are 12 cm and 24 cm.

b).

Let the length of the smaller base of the trapezoid be equal to X cm, then the length of the larger base, by condition, is equal to 3 * X cm.

The length of the midline of the trapezoid is equal to half the sum of the lengths of its bases.

Then 18 = (X + 3 * X) / 2.

4 * X = 36.

X = 36/4 = 9.

The length of the smaller base is 9 cm.

The length of the larger base is 3 * 9 = 27 cm.

Answer: The bases of the trapezoid are 9 cm and 27 cm.



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