The diagonal of an isosceles trapezoid with a perimeter of 52 cm bisects the obtuse angle of the trapezoid.

| March 1, 2021 | education

The diagonal of an isosceles trapezoid with a perimeter of 52 cm bisects the obtuse angle of the trapezoid. Find the lengths of the sides of the trapezoid if the base lengths are 1: 4

By condition, AC is the bisector of the BCD angle, then the BCA angle = DCA. Angle CAD = BCA as criss-crossing angles at the intersection of parallel straight lines BC and AD, then angle CAD = DCA, and then triangle ADC is isosceles, AD + CD.

Let the base BC = X cm, then according to the condition, based AD = 4 * X cm, and therefore the side of the SD = 4 * X cm.

Since the trapezoid is isosceles, then AB = CD = 4 * X cm.

Determine the perimeter of the trapezoid: Ravsd = AB + BC + CD + AD = 4 * X + X + 4 * X + 4 * X = 52.

13 * X = 52.

X = BC = 52/13 = 4 cm.

Then AB = CD = AD = 4 * 4 = 16 cm.

Answer: BC = 4 cm, AB = CD = AD = 16 cm.



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