Using Pythagoras' theorem on triangles ABD and ACD: Let BD = x and DC = y, so BC = x + y. From triangle ABD: AB² = AD² + BD² 13² = 12² + x² 169 = 144 + x² x² = 25 → x = 5 cm. From triangle ACD: AC² = AD² + DC² 14² = 12² + y² → 196 = 144 + y² y² = 52 → y = √52 ≈ 7.21 cm. BC = x + y = 5 + 7.21 = 12.21 cm.
18 19 34 111 428 2165 ?
... -1, 5, 23, 59, ?
13 7 8 13.5 29 ? 228
72, 90, 110, ?, 156, 182, 210
41, 82, ?, 984, 4920, 29520
72, 216, 54, 270, ?, 315
What will come in place of the question mark (?) in the following series?
24, 25, 34, 59, 108, 189, ?
23 40 67 104 ? 208
...50, 64, 80, 98, 118, ?
12, 16, ?, 48, 76, 112
