In a rectangle, the intersection of the diagonals is 4 cm farther from the smaller side

| April 20, 2021 | education

In a rectangle, the intersection of the diagonals is 4 cm farther from the smaller side than from the larger side. The perimeter of the rectangle is 56 cm. Find the sides of the rectangle.

Let a rectangle ABCD be given, in which O is the point of intersection of the diagonals AC and BD, and the distance from point O to the larger side AD is OK = x cm, then:

2 ∙ х (cm) – the length of the smaller sides of the rectangle AB and CD, since point O is equidistant from opposite sides;

x + 4 (cm) – the distance from point O to the smaller side AB, since point O is 4 cm farther from the smaller side than from the larger side;

2 ∙ (x + 4) (cm) – the length of the large sides of the rectangle BC and AD.

Knowing that the perimeter of the rectangle is 56 cm, we compose the equation:

2 ∙ (2 ∙ x + 2 ∙ (x + 4)) = 56;

x = 5;

2 ∙ 5 = 10 (cm) – the length of the smaller sides AB and CD;

2 ∙ (5 + 4) = 18 (cm) – the length of the long sides BC and AD.

Answer: the lengths of the sides of the rectangle are 10 cm and 18 cm.



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