Find the height of the trapezoid if its bases are 14 and 42 cm, and the sides are 17 and 25 cm.

1. A, B, C, d – the tops of the trapezoid. ВС and AD are 14 cm and 42 cm, respectively. AB = 17 cm.

CD = 25 cm.

2. From the peaks B and C we draw the heights ВН and СK.

3. We take the length of the segment AH as x.

The length of the segment KH = 14 cm.

The length of the segment DK = 42 – 14 – x = (28 – x) cm.

4. BH² = AB² – AH² (by the Pythagorean theorem)

BH² = 17² – x² = 289 – x².

СK2 = СD2 – DK2 (by the Pythagorean theorem).

СK² = 25² – (28 – x) ² = 625 – 784 – 56x + x² = 159 – 56x – x².

5. The heights of the СK and ВН are equal.

6.289 – x² = 159 – 56x + x².

56x = 448.

x = 8.

BH² = 17² – x² = 289 – 64 = 225.

BH = √225 = 15 cm.

Answer: the height of the trapezoid is 15 cm.

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