In a quadrangle ABCD AB = x cm. BC is 1 cm less than AB; CD is 1.52 times more than AB; AD is 1 cm larger than CD.

| April 30, 2021 | education

In a quadrangle ABCD AB = x cm. BC is 1 cm less than AB; CD is 1.52 times more than AB; AD is 1 cm larger than CD. Make an equation knowing that the perimeter of ABCD is 12.6 cm. Solve the resulting equation. Find the lengths of all sides of the quadrilateral ABCD.

So, according to the conditions of the problem, it is known that the side AB = x cm.According to the same conditions of the problem, the other sides of the quadrangle will be equal: BC = (x – 1) cm, CD = 1.52x cm and AD = (1.52x + 1) cm.Based on this and the fact that the perimeter of the quadrangle is 12.6 cm, we will compose an equation and solve it:

x + (x – 1) + 1.52x + (1.52x + 1) = 12.6,

x + x – 1 + 1.52x + 1.52x +1 = 12.6,

x + x + 1.52x + 1.52x = 12.6 + 1 – 1,

5.04x = 12.6,

x = 12.6 / 5.04,

x = 2.5.

Hence, side AB = 2.5 cm.Let’s find side BC:

BC = 2.5 – 1 = 1.5 cm.

Find CD:

CD = 1.52 * 2.5 = 3.8 cm.

Find the AD side:

AD = 3.8 + 1 = 4.8 cm.

Answer: The lengths of the sides of the quadrangle ABCD are equal: AB = 2.5 cm, BC = 1.5 cm, CD = 3.8 cm and AD = 4.8 cm.



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