# Trapezoid ABCD, angle A = 90 degrees, MH – middle line of the trapezoid = 18 cm

Trapezoid ABCD, angle A = 90 degrees, MH – middle line of the trapezoid = 18 cm. Angle BCD = 135 degrees, BC refers to AD as 1 to 8. Find AB

1. By the condition of the problem BC / AD = 1/8. Therefore, AD = 8BC.

2. Calculate the length of the base of the trapezoid using the formula for calculating the midline:

(ВС + АD) / 2 = 18 cm.

BC + AD = 36 cm.

3. Substitute 8BC instead of AD into this expression:

BC + 8BC = 36 cm.

BC = 4 cm.

AD = 4 x 8 = 32 cm.

4. From the top of C we draw the height CH.

∠DСН = 135 ° – 90 ° = 45 °.

5.DН = АD – ВС = 32 – 4 = 28 cm.

DН / СН = tangent ∠DСН = 1.

DH = CH = 28 cm.

6. CH = AB = 28 cm (the opposite sides of the rectangle ABCH are equal.

Answer: AB = 28 cm.

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