In a quadrilateral ABCD, side AB = x cm Express the remaining sides of this quadrilateral if:

| June 20, 2021 | education

In a quadrilateral ABCD, side AB = x cm Express the remaining sides of this quadrilateral if: BC is 3 cm less than AB CD is 1.123 times more AB AD 3 cm more than CD Make an equation, knowing that the perimeter of ABCD is 10.2 cm Solve the result the equation. Find the length AB.

Decision.
AB = x cm, then BC = x – 3 (cm), CD = 1.123x (cm), AD = 1.123x + 3 (cm).
The perimeter of a quadrilateral is equal to the sum of the lengths of all its sides, then we can write that
x + (x – 3) + 1.123x + 1.123x +3 = 10.2.
Let’s solve the equation.
x + x – 3 + 1.123x + 1.123x + 3 = 10.2;
2x + 2.246x = 10.2;
4.246x = 10.2;
4.246x = 10.2: 4.246;
x = 2.4.
Hence, AB = 2.4 cm.
Answer: 2.4 cm.

We check, AB = 2.4 cm, then BC = 2.4 – 3 = -0.6 (cm). The side of a quadrangle cannot be negative. This means that the problem has been solved incorrectly.



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