The length of one of the lateral sides of a rectangular trapezoid is 25. Find the length of the largest of the bases

| February 1, 2021 | education

The length of one of the lateral sides of a rectangular trapezoid is 25. Find the length of the largest of the bases of this trapezoid, if it is known that a circle with a radius of 12 can be inscribed into it.

Since a circle is inscribed in the trapezoid, the sum of the lengths of its bases is equal to the sum of the lengths of the lateral sides. AB + СD = BC + AD.

The height of a rectangular trapezoid is equal to the diameter of the inscribed circle, then AB = CH = 2 * R = 24 cm, then СD, by condition, is 25 cm.

In a right-angled triangle СDН, according to the Pythagorean theorem, DН^2 = СD^2 – CH^2 = 625 – 576 = 49.

DН = 7 cm.

The perimeter of the trapezoid is: P = AB + СD + BC + AD = 24 + BC + 25 + AН + 7 = 98.

2 * BC = 98 – 56 = 42.

BC = 42/2 = 21 cm.

Then AD = 21 + 7 = 28 cm.

Answer: The length of the larger base is 28 cm.



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