3. Tokkoon tokkoo lakkoofsota sadee armaan gaditti kennamanii dheerina rogoota rogsadee kofa sirrii ta'uufi ta'uu dhabuu isaanii murteessi. \( \begin{array}{ll}\text { a. } 14 \mathrm{~cm}, 16 \mathrm{~cm}, 18 \mathrm{~cm} & \text { b. } 2 \sqrt{5} \mathrm{~cm}, 2 \mathrm{~cm}, 4 \mathrm{~cm} \\ \text { c. } 3 \mathrm{~cm}, 2 \sqrt{10} \mathrm{~cm}, 7 \mathrm{~cm} & \text { d. } 1.5 \mathrm{~cm}, 2 \mathrm{~cm}, 2.5 \mathrm{~cm} \\ \text { c. } 21 \mathrm{~cm}, 5 \mathrm{~cm}, 25 \mathrm{~cm} & \text { f. } 6 \mathrm{~m}, 9 \mathrm{~cm}, 12 \mathrm{~cm}\end{array} \)

a. For sides \(14\text{ cm}\), \(16\text{ cm}\), and \(18\text{ cm}\): - Check: - \(14+16=30>18\) - \(14+18=32>16\) - \(16+18=34>14\) Since every pair sums to more than the third side, these lengths form a valid triangle. --- b. For sides \(2\sqrt{5}\text{ cm}\), \(2\text{ cm}\), and \(4\text{ cm}\): - Note that \(2\sqrt{5}\approx4.472\text{ cm}\). - Check: - \(2\sqrt{5}+2\approx4.472+2=6.472>4\) - \(2\sqrt{5}+4\approx4.472+4=8.472>2\) - \(2+4=6>2\sqrt{5}\approx4.472\) All conditions are satisfied, so these side lengths are valid. --- c. For sides \(3\text{ cm}\), \(2\sqrt{10}\text{ cm}\), and \(7\text{ cm}\): - With \(2\sqrt{10}\approx6.324\text{ cm}\): - Check: - \(3+6.324\approx9.324>7\) - \(3+7=10>6.324\) - \(6.324+7\approx13.324>3\) These satisfy the triangle inequality, so they form a valid triangle. --- d. For sides \(1.5\text{ cm}\), \(2\text{ cm}\), and \(2.5\text{ cm}\): - Check: - \(1.5+2=3.5>2.5\) - \(1.5+2.5=4>2\) - \(2+2.5=4.5>1.5\) All conditions hold true, hence these are valid. --- e. For sides \(21\text{ cm}\), \(5\text{ cm}\), and \(25\text{ cm}\): - Check: - \(21+5=26>25\) - \(21+25=46>5\) - \(5+25=30>21\) The triangle inequality is satisfied in every case, so these form a valid triangle. --- f. For sides \(6\text{ m}\), \(9\text{ cm}\), and \(12\text{ cm}\): - First convert \(6\text{ m}\) to centimeters: \(6\text{ m}=600\text{ cm}\). - Now the sides are \(600\text{ cm}\), \(9\text{ cm}\), and \(12\text{ cm}\). - Check: - \(600+9=609>12\) - \(600+12=612>9\) - \(9+12=21\quad\) but \(21 \not>600\) Since \(9+12\) is not greater than \(600\), these lengths do not satisfy the triangle inequality and cannot form a valid triangle.