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victus00 [196]
3 years ago
11

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.

Mathematics
1 answer:
Brut [27]3 years ago
6 0
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.

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Anna007 [38]

Choice C is the correct answer because

\frac{(6+2)^3-12}{5}\\\\\frac{(8)^3-12}{5}\\\\\frac{512-12}{5}\\\\\frac{500}{5}\\\\100\\\\

So in short, \frac{(6+2)^3-12}{5}=100\\\\

------------------------------------------

The mistake Jerry likely made was that he only cubed the 2 and didn't realize the 6 was part of that cubing process. It seems he didn't add first and decided to cube before adding.

This is probably what steps Jerry did

\frac{6+2^3-12}{5}\\\\\frac{6+8-12}{5}\\\\\frac{14-12}{5}\\\\\frac{2}{5}\\\\

But as mentioned, those steps are incorrect because the 6 is part of the cubing operation. In other words, Jerry should have added the 6+2 first before cubing afterward (due to PEMDAS determining the order of operations).

Or you could think of it like this

\frac{(6+2)^3-12}{5}\\\\\frac{(6+2)(6+2)(6+2)-12}{5}\\\\\frac{(8)(8)(8)-12}{5}\\\\\frac{512-12}{5}\\\\\frac{500}{5}\\\\100

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2 years ago
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