The length of a rectangle is #5 ft# less than twice the width, and the area of the rectangle is #52 ft^2#. What is the dimension of the rectangle?

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Answer 1 · 2017-07-21T08:59:19

#"Width" = 6 1/2 ft and " length " = 8 ft#

Define the length and width first.

The width is shorter, so let that be #x#

The length is therefore: #2x-5#

The area is found from #A = l xx b# and the value is #52#

#A = x xx (2x-5) =52

#A = 2x^2 -5x=52#

#2x^2 -5x-52=0" "larr# find factors

#(2x-13)(x+4)=0#

#2x-13=0" "rarr 2x=13" "x = 13/2 = 6 1/2#

#x+4=0" "rarr x =-4" "larr# reject as invalid

If the width is #6 1/2# the the length is:

#2 xx 6 1/2-5 =8#

Check:

#6 1/2 xx 8=52#