matt's rectangular patio measures 9 by 12 feet. he wants to increase the patios dimensions so its area will be tiwce the area it is now. he plans to increase both the length and the width by the same amount,x. find x to the nearest hundreth of a foot.
2007-06-03 09:15:53 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
So we wish
(9+x)(12+x) = 2*9*12
9*12 + 21x + x^2 = RHS
x^2 + 21x - 108 = 0
x = 4.273 feet
2007-06-03 09:26:59 · answer #1 · answered by Dr D 7 · 1⤊ 0⤋
9 times 12 = 108 sq ft
(9+x) times (12+x) = 2 times 108 = 216
You need to multiply 9+X times 12+X
Did you get x^2 + 21X + 108? (If not, try again.)
So your equation to solve becomes-
X^2 + 21X + 108 = 216, or
X^2 + 21X - 108 = 0
To solve, use the quadratic equation formula.
X = 4.2733 or 4.27 to the nearest hundreth of a foot.
Check-
13.27 x 16.27 = 215.90
2007-06-03 16:42:24 · answer #2 · answered by skipper 7 · 0⤊ 0⤋
Current area = 108 sq. ft. (9 x 12)
Desired area = 216 sq. ft. (2 x 108)
Increasing each side by the same #, then multiplying them to find desired area. Multiply out the quadratic and solve for x.
(9+x)(12+x) = 216
108 + 9x + 12x + x^2 = 216
x^2 + 21x -108 = 0 (To get this, I rearranged terms, subtracted 216 from each side)
Use quadratic formula to solve
(-21 +/- 29.55)/2 = ~4.27 feet added to each side.
New dimensions = 13.27 and 16.27
Double Check 13.27 x 16.27 = 205.9029
2007-06-03 16:27:00 · answer #3 · answered by booboo559 2 · 0⤊ 0⤋
2*9*12 = (9+x)(12+x)
so
108= 21x+x^2 and x^2+21x-108=0
x=((-21+-sqrt(873))/2 = 4.27 feet ( x can´t be negative)
2007-06-03 16:29:24 · answer #4 · answered by santmann2002 7 · 0⤊ 0⤋