In a rectangular trapezoid, the smaller side is 12 cm and the larger one makes an angle of 45 °

| February 25, 2021 | education

In a rectangular trapezoid, the smaller side is 12 cm and the larger one makes an angle of 45 ° with a large fit. find the base of the trapezoid if its midline is 20 cm.

Let ABCD be a given trapezoid, AB is perpendicular to BC and AD, AB = 12 cm. Angle D = 45 °. Middle line = 20 cm.

Let’s draw the height СН, it is equal to AB, СН = AB = 12 cm.Consider the triangle CHD: angle Н = 90 ° (СН – height), angle D = 45 ° (by condition), hence the angle C = 45 ° (180 – 90 – 45 = 45). This means that the triangle CHD is isosceles, CH = HD = 12 cm.

Let the base of BC be equal to x, then the base of AD = x + 12 (since it consists of two segments AH and HD).

Let’s express the middle line:

(BC + AD) / 2 = 20.

(x + x + 12) / 2 = 20.

(2x + 12) / 2 = 20.

x + 6 = 20.

x = 14 (cm) – BC base.

AD = x + 12 = 14 + 12 = 26 (cm).

Answer: the bases of the trapezoid are 14 cm and 26 cm.



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