A rectangle has a length of 26 feet less than 10 times its width. If the area of the rectangle is 8804 square feet, what is the length of the rectangle?

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Answer 1 · 2018-02-23T06:19:01

The Length ,# L = 284 ft.#

Given:
Rectangle

Area, #A = 8804 ft^2#

let W bet he width of the rectangle

  L be the length of the rectangle

#L= 10W-26# # Equation 1#

substitute to #equation 2#

#A =( L)(W)# #equation 2#

#A = ( 10W-26)(W)#

# 8804 = ( 10W-26)(W)#

factor

# 8804 =2 ( 5W-13)(W)#

divide both sides by 2

#4402 = ( 5W-13)(W)#

#4402 = 5W^2 - 13W#

transposing 4402 to the right side of the equation

#0 = 5W^2 - 13W -4402#

by quadratic formula

#W ={ -(-13) +sqrt[ (-13)^2 - 4(5)(-4402)]}/(2(5)#

#W ={[ 13 +sqrt[169 +88040)]}/10#

#W =[13 +(sqrt88209)]/10#

#W= (13+ 297)/10#

#W = 310/10#

#W = 31# ft

Thus , # L = 10W-26 = 10(31)- 26#

# L = 284 ft.# answer

#W ={ -(-13) -sqrt[ -(-13^2) - 4(5)(-4402)]}/(2(5)#

this is discarded since this will yield a negative answer.