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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