A rectangle with an area of #120# #i n^2# has a length #8# inches longer than two times its width. What is the width of the rectangle?

1 Answer
Jul 1, 2016

#6# inches

Explanation:

Area of a rectangle with length, l and breadth, b = #l*b#

Given # l = 2b + 8# and #A = 120#

Area A = #l* b = (2b + 8)*b = 2b^2 + 8b = 120 # =>

#2b^2 + 8b - 120 = 0# =>

#b^2 + 4b - 60 = 0# =>

# b^2 + 10b - 6b - 60 = 0# =>

# b(b+10) -6 (b+10) = 0# =>

# (b-6)(b+10) = 0#; =># b = 6# as #b# cannot be #-10#.

Width is # 6 # inches