The perimeter of the triangle ABD is 12 cm. The perimeter of the triangle BDC is 30 cm. The perimeter of the quadrilateral ABCD is 32 cm. Find BD.
Perimeter of triangle ABD: P1 = | AB | + | BD | + | DA | = 12 cm;
Perimeter of triangle BDC: P2 = | BD | + | DC | + | CB | = 30 cm;
The perimeter of the quadrilateral ABCD: P3 = | AB | + | BC | + | CD | + | DA | = 32 cm.
Comparing the expressions for the perimeters P1, P2 and P3, we get that
A1 + A2 = A3 + 2 × | BD |.
Thus, the required length of the segment BD is:
| BD | = (P1 + P2 – P3) / 2 = (12 + 30 – 32) / 2 = 5 cm.
Answer: The length of the segment BD is 5 cm.
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