Write an equation and solve: One leg of a right triangle is thee more feet than the other leg. The hypotenuse is 12 feet. How long is the shorter leg?
This is what I have:
1.x^2 + ( x + 3)^2 = 12^2
2.2x^2 + 6x + 9 = 144
3.2x^2 +6x -135 =0
4.now what? Quadratic?
2006-08-05 09:59:44 · 7 answers · asked by sabrina s 2 in Science & Mathematics ➔ Mathematics
I think this is probably done, but I'll do it my way -- completing the square, starting with what you already had. (That's correct, by the way.)
x^2 + (x + 3)^2 = 12^2
2x^2 + 6x + 9 = 144
2x^2 + 6x = 135
x^2 + 3x = 135/2
x^2 + 3x + (3/2)^2 = 135/2 + 9/4 = (270 + 9)/4
(x + 3/2)^2 = 279/4
x + 3/2 = (1/2) sqrt(279)
x = [-3 + sqrt(279)] / 2 = 6.85 feet
So the longer leg is 9.85 feet, and the hypoteneuse is
sqrt(6.85^2 + 9.85^2) = sqrt(143.945) = 11.998 = 12
2006-08-05 12:17:41 · answer #1 · answered by bpiguy 7 · 3⤊ 0⤋
First, the relationship between the legs and hypotenuse of t he triangle:
(leg one)^2 + (leg two)^2 = (hypotenuse)^2
AKA
a^2 + b^2 = c^2
So, according to the question
Leg one: "x"
Leg two: "x + 3"
Hypotenuse: 12
x^2 + (x + 3)^2 = 12^2
x^2 + x^2 + 6x + 9 = 144
2x^2 + 6x + 9 = 144
or answer # 2
2006-08-05 21:53:03 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Yup. Use the quadratic formula for the 'standard form' quadratic: ax^2+bx+c=0
The roots of which are given by:
x=((-b (+/-) sqrt(b^2-4ac))/(2a)
In this case, a=2, b=6 and c= -135
This will give you two roots:
6.8516465442450328831792069483778
and
-39.406586176980131532716827793511
(Use your calculator or the one in Windows)
Since a negative distance has no real meaning (in this problem) it is an 'extraneous' root.
The two legs are then:
6.8516465442450328831792069483778
and
9.8516465442450328831792069483778
Check 6.85164....^2 + 9.85164.....^2 = 143.999999.....
You had the right instincts. Trust them. The more you use them, the better they get and the better your insights will become.
Doug
2006-08-05 17:33:50 · answer #3 · answered by doug_donaghue 7 · 1⤊ 0⤋
Yes, go to the quadratic formula. Your work is perfect so far.
2006-08-05 17:04:32 · answer #4 · answered by jenh42002 7 · 0⤊ 0⤋
You did everything great - now use the quadratic formula because this doesn't factor.
2006-08-05 20:54:47 · answer #5 · answered by MollyMAM 6 · 0⤊ 0⤋
3.2x^2 + 6x - 135 = 0
b^2- 4ac = (6)^2 - 4(2)(-135) = 1116 (our equaiton has two distinct real roots)
x = [-b +/- root(b^2 - 4ac)]/2a
x = [-6 +/- root(1116)]/2(2)
x = [-6 +/- 33.04]/4 (discard the negative answer)
x = [27.4]/2
x = 13.7 feet
2006-08-05 17:11:24 · answer #6 · answered by hackmaster_sk 3 · 0⤊ 0⤋
I would go with the quadratic formula. I don't think this can be factored.
2006-08-05 17:04:39 · answer #7 · answered by I Know Nuttin 5 · 0⤊ 0⤋