Anyone know how to solve it?

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Answer 1 · 2018-05-05T16:24:08

#x < 8#

From both diagrams, we can find #x# by comparing both area of triangle and area of rectangle together with the statement connecting both diagrams..

The statement implies that;

Area of rectangle less than Area of triangle

Area of rectangle #= "length" xx "breadth"#

Area of triangle#= 1/2 "base" xx "height"#

Hence;

#lb < 1/2bh#

#12 xx (x + 2) < 1/2 xx (x + 16) xx 10#

#12x + 24 < ((x + 16) (10))/2#

#12x + 24 < (10x + 160)/2#

#12x + 24 < (10x)/2 + 160/2#

#12x + 24 < 5x + 80#

Collecting like terms..

#12x - 5x < 80 - 24#

#7x < 56#

Dividing both sides by #7#

#(7x)/7 < 56/7#

#(cancel7 x)/cancel7 < 56/7#

#x <56/7#

#x < 8#