The angles at one of the bases of the trapezoid are 44 degrees and 46 degrees, and the segments connecting

| February 17, 2021 | education

The angles at one of the bases of the trapezoid are 44 degrees and 46 degrees, and the segments connecting the midpoints of the opposite sides of the trapezoid are 44 cm and 46 cm. Find the bases of the trapezoid.

Let us extend the lateral sides of the trapezoid to their intersection at point O. Consider the triangle AOD. AOD angle = 180 – 44 – 46 = 90. AOD triangle is rectangular.

Let the smaller base of the trapezoid be BC = 2 * X cm, and the larger BP = 2 * Y cm.

Since the segment РK, by condition, connects the midpoints of the bases of the trapezoid, then OK is the median of the AOD triangle, and OP is the median of the BOS triangle.

In a right-angled triangle, the median drawn from the apex of the right angle is half the hypotenuse. OВ = BC / 2 = X, OK = AD / 2 = Y.

Then OK = OP + РK = X + 44 = Y.

Y = X + 44. (1).

MH, by condition, is the middle line of the trapezoid, then MH = (BP + BC) / 2 = (2 * X + 2 * Y) / 2 = 46.

X + Y = 46 (2).

Let’s solve the system of equations 1 and 2.

X + X + 44 = 46.

2 * X = 2 cm.

X = 1 cm.

BC = 2 * X = 2 cm.

Y = 46 – 1 = 45 cm.

AD = 2 * Y = 90 cm.

Answer: BP = 90 cm, BC = 2 cm



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