The bases of the trapezoid are 6 and 34, the area of the trapezoid is 300, and one of the sides is 25.
| August 30, 2021 | education
The bases of the trapezoid are 6 and 34, the area of the trapezoid is 300, and one of the sides is 25. Find the second side of the trapezoid.
Let us lower the height CH from the top of the trapezoid.
The area of the trapezoid is: S = (AD + BC) * CH / 2.
300 = (34 + 6) * CH / 2.
CH = 600/40 = 15 cm.
In the triangle СНD, we define, according to the Pythagorean theorem, the leg DH.
DH ^ 2 = CD ^ 2 – CH ^ 2 = 25 ^ 2 – 15 ^ 2 = 625 – 225 = 400.
DН = 20 cm.
Determine the length of the segment AK.
AK = AD – KH – DH = 34 – 6 – 20 = 8 cm.
In a right-angled triangle ABK, we determine the length of the hypotenuse AB.
AB ^ 2 = BK ^ 2 + AK ^ 2 = 15 ^ 2 + 8 ^ 2 = 225 + 64 = 289.
AB = 17 cm.
Answer: Lateral side AB = 17 cm.
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