SOLUTION: you are planning a rectangular patio with length that is 7 ft less than three times its width.The area of the patio is 120 ft^2. What are the dimensions of the patio

Algebra ->  Rectangles -> SOLUTION: you are planning a rectangular patio with length that is 7 ft less than three times its width.The area of the patio is 120 ft^2. What are the dimensions of the patio      Log On


   

Question 865124: you are planning a rectangular patio with length that is 7 ft less than three times its width.The area of the patio is 120 ft^2. What are the dimensions of the patio
Found 2 solutions by josgarithmetic, mananth:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
L=3w-7
wL=120
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w%283w-7%29=120
3w%5E2-7w-120=0
Discriminant is %28-7%29%5E2%2B4%2A3%2A120=49%2B12%2B120=49%2B1440=1489, a prime number.
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highlight%28w=%287%2Bsqrt%281489%29%29%2F6%29
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Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
width -------xft
length 3x-7 ft
area = L * W
120 =x(3x-7)
120=3x^2-7x
3x^2-7x-120=0
use the formula method
a= 3 b= -7 c= -120

b^2-4ac= 49 - -1440
b^2-4ac= 1489 sqrt%28%091489++++%09%29= 38 3/5
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( 7 + 38 3/5 )/ 6
x1= 7 3/5
x2=( 7 -38 3/5 ) / 6
x2= -5 1/4
Ignore negative value mph
x = 7 3/5
width = 7 3/5
length =3*(38/5) -7
=15 4/5 feet