Find the smaller base of the trapezoid and its midline, if the larger base is 16 cm, and the smaller base is 6 cm less than the midline?
| March 8, 2021 | education
Decision.
Let the smaller base of the trapezoid be equal to X cm, then by the condition of the problem the middle line is equal to X + 6.
The middle line of the trapezoid is equal to half the sum of the bases. Means
(16 + X) / 2 = X + 6.
We solve the equation:
16 + X = 2 * (X + 6);
16 + X = 2X + 12;
2X – X = 16 – 12;
X = 4.
The smaller base is 4 cm.
Accordingly, the middle line is 4 + 6 = 10 cm.
Answer: the smaller base of the trapezoid is 4 cm, and its middle line is 10 cm.
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