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Answer 1 · 2017-11-08T04:26:24

length #= 14# m
and
width #= 8#m

Let the length of the rectangle be #l# and width be #w#,

Given that: The width of a rectangle is six meters less than its length.

#=> w = l- 6#m

Also #Area = 112 m^2#

Area = length x width

#=> l xx w = 112#

#=> l xx(l-6) =112#

#=> l^2 - 6l =112#

#=> l^2 - 6l -112 = 0 #

Solve this quadratic equation:

#=> l^2 -14l +8l - 112=0#

#=> l(l-14) + 8( l -14) =0 #

#=> (l-14) (l+8)= 0#

#=> l= 14 or l= -8#

As dimensions cannot be negative, we take #l = 14#

So, length =# 14m #

and width = #l-6= 14-6=8m#

Answer: length #= 14# m
and
width #= 8#m