In an isosceles trapezoid, side 52, height 48, midline 30. Find its larger base.

1. A, B, C, D – the tops of the trapezoid. BH – height. MK is the middle line.

2. Calculate the length of the segment AH:

AH = √AB²-BH².

AH = √52²- 48² = √2704²- 2304 = √400 = 20 units.

3. АН = (АD – ВС) / 2 (according to the properties of an isosceles trapezoid).

АD – ВС = 20 х 2 = 40 units of measurement.

4. MK = (AD + BC) / 2 = 30.

AD + BC = 60 units.

5. Add the expressions from point 3 and point 4:

2AD = 100.

AD = 50 units.

Answer: AD = 50 units of measurement – the larger the base of the trapezoid.



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