In an isosceles trapezoid, the middle line is 5 cm, and the larger base is 18 cm

| August 14, 2021 | education

In an isosceles trapezoid, the middle line is 5 cm, and the larger base is 18 cm less than the perimeter. Find the perimeter if the diagonal bisects the obtuse angle.

Since the AC diagonal divides the obtuse angle in half, it is the bisector of the BCD angle.

BCA angle = DCA.

Angle BCA = CAD as criss-crossing angles at the intersection of parallel straight lines BC and AD secant AC. Then the angle DСА = DАС, and the triangle АСD is isosceles.

Then AD = CD = AB.

Let AB = CD = AD = X cm, BC = Y cm.

Since the middle line of the trapezoid is 5 cm, then (X + Y) / 2 = 5.

(X + Y) = 10 cm. (1)

According to the condition of Ravsd – 18 = HELL = H.

3 * X + Y – 18 = X.

2 * X + Y = 18. (2).

Let’s solve the system of equations 1 and 2.

Y = 10 – X.

2 * X + 10 – X = 18.

X = AB = CD = AD = 8 cm.

BC = 10 – 8 = 2 cm.

Then P = 3 * 8 + 2 = 26 cm.

Answer: The perimeter of the trapezoid is 26 cm.



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