In trapezoid ABCD, base BC = 10, AD = 4. On base BC, point M is chosen so that segment DM

| February 8, 2021 | education

In trapezoid ABCD, base BC = 10, AD = 4. On base BC, point M is chosen so that segment DM divides the area of trapezoid ABCD in half. In what ratio does point M divide BC from point B?

Let the length of the segment BM = X cm, then the length of the segment CM = (10 – X) cm.

Let us draw the height of the BP, which is the height of the triangle and the height of the ADMВ trapezoid.

Determine the area of the triangle СDM.

Ssdm = CM * DН / 2 = (10 – X) * DN / 2.

Let us determine the area of the trapezium ADMВ.

Sadmv = (АD + ВM) * DН / 2 = (4 + X) * DН / 2.

Since, by condition, these areas are equal, then

(10 – X) * DН / 2 = (4 + X) * DН / 2.

10 – X = 4 + X.

2 * X = 6.

X = BM = 3 cm.

Then CM = 10 – 3 = 7 cm.

ВM / CM = 3/7.

Answer: Point M divides the segment in the ratio of 3/7.



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