In an isosceles trapezoid, the base of AD is 4 cm larger than the base of BC.
| August 21, 2021 | education
In an isosceles trapezoid, the base of AD is 4 cm larger than the base of BC. The lateral side is 3 cm. Find the base of the trapezoid if you know that you can inscribe a circle into it
1. Since a circle is inscribed in an isosceles trapezoid, according to its properties:
AB + CD = BC + AD.
2. AB = CD = 3 centimeters, since the sides of an isosceles trapezoid are equal.
AB + CD = 6 centimeters.
BC + AD = 6 centimeters.
3. According to the condition of the problem, AD is more than BC by 4 centimeters, that is, AD = BC + 4 cm.
BC + BC + 4 = 6 centimeters.
2 BC = 2 centimeters.
BC = 1 centimeter.
AD = BC + 4 = 1 + 4 = 5 centimeters.
Answer: BC = 1 centimeter, AD = 5 centimeters.
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