A circle with a radius of 4 m is inscribed in a rectangular trapezoid, the difference between the bases of the trapezoid is 6 m. Nastya is the perimeter of the trapezoid.
In order to solve this problem, you need to draw a picture of this situation or imagine it in your mind. Then conduct a detailed analysis. If the circle is inscribed, then its diameter is the height of the trapezoid, one side is lateral, where the right angle is:
4 * 2 = 8 cm.
The sum of the bases is equal to the sum of the sides. If we lower the perpendicular from the top of the smaller base to the larger side, then we get a right-angled triangle, one leg = 6 cm, the other 8 cm. By the Pythagorean theorem, we find 6² + 8² = 100, √100 = 10 cm – this is the second side.
P = (10 + 8) * 2 = 36 cm.
Therefore, our answer is 36cm.
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