In a rectangular trapezoid, the area is 30 cm2, the perimeter is 28 cm, and the smaller side is 3 cm. Find the larger side.
The area of the trapezoid is equal to the product of the half-sum of the bases and the height.
Since the trapezoid is rectangular, the height of the trapezoid is equal to its side AB, then:
S = (AD + BC) * AB / 2.
30 = (AD + BC) * 3/2.
(АD + ВС) = 20 cm.
The perimeter of the trapezoid is:
P = AB + BC + CD + AD.
P = (AD + BC) + AB + CD.
Since (AD + BC) = 20 cm, then
28 = 20 + 3 + CD.
СD = 28 – 23 = 5 cm.
Answer: The large side is 5 cm.
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