The diagonal of the rectangle CDEF intersect at point K. Find the sides of the rectangle if its perimeter is 28 cm

| February 4, 2021 | education

The diagonal of the rectangle CDEF intersect at point K. Find the sides of the rectangle if its perimeter is 28 cm, and the perimeter of triangles CDK and DEK are 16 cm and 18 cm.

Since CDEF is a rectangle, its diagonals are equal and at the point of intersection they are halved.

CK = DK = EK = FK.

Let the sides CD and EF of the rectangle be equal to X, and the sides DE and CF equal to Y, and the segments CK = DK = EK = FK = Z.

Then Рcdef = 2 * X + 2 * Y = 28 cm. (1).

Pcdk = X + 2 * Z = 16 cm. (2).

Pdek = Y + 2 * Z = 18 cm. (3).

In equations 2 and 3, we express 2 * Z and equate them.

2 * Z = 16 – X.

2 * Z = 18 – Y.

16 – X = 18 – Y.

X = Y – 2.

Substitute this value in Equation 1.

2 * (Y – 2) + 2 * Y = 28.

4 * Y = 28 + 4 = 32.

Y = 24/4 = 8 cm.

Then X = 8 – 2 = 6 cm.

Answer: The sides of the rectangle are 8 cm and 6 cm.



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