Write True or False against each of the following statements: |
(a) \[16:24::20:30\] |
(b) \[~21:6::35:10\] |
(c) \[12:18::28:12\] |
(d) \[8:9::24:27\] |
(e) \[5.2:3.9::3:4\] |
(f) \[0.9:0.36::10:4\] |
Answer:
(a) \[16:24::20:30\] Product of extremes \[=16\times 30=480\] Product of middle terms \[=24\times 20=480\] Therefore, product of extremes = product of middle terms Hence, \[16:24::20:30\] is True. (b) \[21:6::35:10\] Product of extremes \[=21\times 10=210\] Product of middle terms \[=6\times 35=210\] Therefore, product of extremes = product of middle terms Hence, \[21:6::35:10\] is True. (c) \[12:18::28:12\] Product of extremes \[=12\times 12=144\] Product of middle terms \[=18\times 28=504\] Therefore, product of extremes \[\ne \] product of middle terms \[(12\times 12\ne 18\times 28)\] Hence \[12:18::28:12\] is False. (d) \[8:9::24:27\] Product of extremes \[=8\times 27=216\] Product of middle terms \[=9\times 24=216\] Therefore, product of extremes = Product of middle terms Hence, \[8:9::24:27\] is True. (e) \[5.2:3.9::3:4\] Product of extremes \[=5.2\times 4=20.8\] Product of middle terms \[=3.9\times 3=11.7\] Therefore, product of extremes ^ product of middle terms Hence \[5.2:3.9::3:4\] is False. (f) \[0.9:0.36::10:4\] Product of extremes \[=0.9\times 4=3.6\] Product of middle terms \[=0.36\times 10=3.6\] Therefore, product of extremes = product of middle terms Hence \[0.9:0.36::10:4\] is True.
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