A circle (AD and BC-bases) is inscribed in a rectangular trapezoid ABCD, CD is perpendicular to AD
| January 29, 2021 | education
A circle (AD and BC-bases) is inscribed in a rectangular trapezoid ABCD, CD is perpendicular to AD, angle A = 30 degrees. The perimeter of the trapezoid is 24 cm. What are the sides AB and CD.
Let’s lower the height of the ВК to the base of the blood pressure. In the resulting triangle ABE, the angle A = 30, therefore the leg BE is equal to half of the hypotenuse AB. BE = СD = AB / 2. AB = 2 * СD.
Since a circle is inscribed in the trapezoid, the sum of the bases of the trapezoid is equal to the sum of the sides of the СD + AB = СВ + AD.
СD + 2 *СD = СВ + AD.
The perimeter of the trapezoid is.
AB * СВ + СD + AD= 24.
СD + 2 * СD + СD + 2 * СD = 24.
6 * СD = 24.
СD = 24/6 = 4 cm.
AB = 2 * 4 = 8 cm.
Answer: AB = 8 cm, СD = 4 cm.
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