The circumference of the described quadrilateral ABCD is 36 cm. Find side AB if it is three times the size of side CD.
| April 18, 2021 | education
Since a circle is inscribed in the quadrilateral ABCD, the sums of the lengths of its opposite sides are equal.
AB + CD = AD + BC.
Ravsd = (AB + CD) + (AD + BC) = 2 * (AB + CD) = 36 cm.
AB + CD = 36/2 = 18 cm.
By condition, AB = 3 * CD.
3 * CD + CD = 18.
CD = 18/4 = 4.5 cm.
AB = 3 * 4.5 = 13.5 cm.
Answer: The length of the AB side is 13.5 cm.
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