A certain right triangle has area 30 in. squared . one leg of the triangle measures 1 in. less than the hypotenuse. let x repres
ent the length of the hypotenuse. a) express the length of the leg mentioned above in terms of x. give the domain of x. b) express the length of the other leg in terms of x. c) write an equation based on the information determined thus far. square both sides and then write the equation with one side as a polynomial with integer coefficients, in descending powers, and the other side equal to 0. divide out any common factors to find the most simplified form. d) solve the equation in part (c) graphically. find the lengths of the three sides of the triangle.
1 answer:
A) The length of the longer leg is x-1
b) Based on the area, the other leg is 2*30/(x -1). Based on the Pythagorean theorem, the other leg is √(x^2 -(x -1)^2).
c) Equating the two expressions for the shorter leg, we have
.. 60/(x -1) = √(2x -1)
.. 3600/(x -1)^2 = (2x -1)
.. (2x -1)(x^2 -2x +1) = 3600
.. 2x^3 -5x^2 +4x -3601 = 0
d) There is one positive real root, at x=13. A graphical solution works well.
The three sides of the triangle are 5 in, 12 in, 13 in.
_____
5-12-13 is a well-known Pythagorean triple. It is the next smallest one after 3-4-5.
b) Based on the area, the other leg is 2*30/(x -1). Based on the Pythagorean theorem, the other leg is √(x^2 -(x -1)^2).
c) Equating the two expressions for the shorter leg, we have
.. 60/(x -1) = √(2x -1)
.. 3600/(x -1)^2 = (2x -1)
.. (2x -1)(x^2 -2x +1) = 3600
.. 2x^3 -5x^2 +4x -3601 = 0
d) There is one positive real root, at x=13. A graphical solution works well.
The three sides of the triangle are 5 in, 12 in, 13 in.
_____
5-12-13 is a well-known Pythagorean triple. It is the next smallest one after 3-4-5.
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Answer:
The key to this question is converting all the mass units to the same unit and adding them all up.
The only value that isn't consistent with the other units is 450 gm or grams.
Recall that 1 gram is equal to 0.001 kilo grams. So if you want to convert grams to kilograms you would multiply that amount by 0.001 or 1/1000
Now let's add up all the masses.
(Now a few footnotes here, that I considered but wasn't sure about. The answer asks for weight, but you're only given mass to work with. That would be fine, if the question asked you to convert it to SI weight units like Newtons, but there's no mention of that. And also I'm not sure if the question requires significant digits. But I'll continue the answer if you think so)
To convert this into weight in Newtons, multiply by 9.81 m/s^2