In rectangle ABCD, the bisector AN of angle BAD divides the side BC into segments: BN = 7 cm and NC = 4 cm

| February 24, 2021 | education

In rectangle ABCD, the bisector AN of angle BAD divides the side BC into segments: BN = 7 cm and NC = 4 cm. Find: 1) the perimeter of the rectangle; 2) the length of the midline of the trapezoid ANCD.

Since АN is the bisector of the angle BAD, the angle BAN = DAN.

The angle DАN is equal to the angle BNА as the intersecting angles at the intersection of parallel lines ВС and АD of the secant АN. Then the angle BNA is equal to the angle BAN, and therefore the triangle ABN is isosceles and AB = BN = 7 cm.

The length of the segment BC = BN + CN = 7 + 4 = 11 cm.

Since ABCD is a rectangle, then AD = BC = 11 cm, AB = CD = 7 cm.

The perimeter of the rectangle is: 2 * (AB + AD) = 2 * (7 + 11) = 36 cm.

Determine the length of the midline of the MР trapezoid.

MP = (AD + NC) / 2 = (11 + 4) / 2 = 15/2 = 7.5 cm.

Answer: The middle line of the trapezoid is 7.5 cm, the perimeter is 30 cm.



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