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?

Question

4377 views around the world

You can reuse this answer
Creative Commons License

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.