question_answer

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.