The midline of the trapezoid is 6 and the base difference is 4. Find the larger base.

Given: ABCD – trapezoid;
ОМ – middle line;
OM = 6 centimeters;
AD – BC = 4 centimeters;
Find the length of the larger base AD -?
Solution:
1) Consider the trapezoid ABCD. If AD – BC = 4, then AD = 4 + BC;
2) Midline OM = (AD + BC) / 2 by definition of the midline. We have been given that OM = 6 centimeters.
Then (АD + ВС) / 2 = 6 (multiply the right and left sides of the equality by the number 2);
AD + BC = 12 (substitute instead of AD = 4 + BC);
4 + BC + BC = 12;
2 * BC = 12 – 4;
2 * BC = 8;
BC = 8: 2;
BC = 4 centimeters – smaller base;
3) AD = 4 + 4;
AD = 8 centimeters – larger base.
Answer: 8 centimeters.



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