Find the height of the trapezoid if its bases are 14 and 42 cm, and the sides are 17 and 25 cm.
| January 28, 2021 | education
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.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
