The two sides of the parallelogram are 3 cm and 5 cm, and one of the diagonals is 4 cm.

| June 10, 2021 | education

The two sides of the parallelogram are 3 cm and 5 cm, and one of the diagonals is 4 cm. Find the distance between the intersection points of the bisectors of the sharp corners of the parallelogram with its smaller diagonal.

The diagonal equal to 4 cm is the smaller diagonal of the parallelogram, which is the leg of the right-angled triangles ABD and BD.

The bisector AO divides the leg BD into segments proportional to the adjacent sides.

AB / AD = BO = DO = 3 * X / 5 * X.

BO = 3 * X, DO = 5 * X.

The bisector CP divides the leg BD into segments proportional to the adjacent sides.

DC / BC = DP = BP = 3 * X / 5 * X.

DP = 3 * X, BP = 5 * X.

OP = DO – DP = 5 * X – 3 * X = 2 * X.

BO + OP + DP = BD = 4 cm.

3 * X + 2 * X + 3 * X = 4 cm.

8 * X = 4.

X = 0.5.

OP = 2 * 0.5 = 1 cm.

Answer: The distance between points O and P is 1 cm.



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