Three consecutive sides of a quadrilateral circumscribed about a circle are related as 2: 5: 7
| August 2, 2021 | education
Three consecutive sides of a quadrilateral circumscribed about a circle are related as 2: 5: 7, the perimeter of a quadrilateral is 54 cm, find its sides
Let side BC = 2 * X, then CD = 5 * X, and side AD = 7 * X.
Since a circle is inscribed in a quadrilateral, the sums of its opposite sides are equal.
AB + CD = BC + AD.
AB + 5 * X = 2 * X + 7 * X.
AB = 9 * X – 5 * X = 4 * X.
Knowing the perimeter of the quadrilateral, we define X.
2 * X + 4 * X + 5 * X + 7 * X = 54.
18 * X = 54.
X = 54/18 = 3.
Then the side AD = 7 * 3 = 21 cm,
CD = 5 * 3 = 15 cm,
BC = 2 * 3 = 6 cm,
AB = 4 * 3 = 12 cm.
Answer: The sides of the quadrangle are 6 cm, 12 cm, 15 cm, 21 cm.
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