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.
You might be interested in
Answer:
<u>1 cup</u> of milk Juan should use.
Step-by-step explanation:
Given:
A recipe calls for 120 ml of milk for each 200 g of flour.
Juan is going to use 1 pound of flour.
Now, to estimate the number of cups of milk.
Let the quantity of milk be
Now, to convert the pound of flour to gram.
1 pound = 453.59 g.
So, Juan is going to use 453.59 g of flour.
As, given recipe calls for 120 ml of milk for each 200 g of flour.
So, 120 ml is equivalent to 200 g.
Thus, is equivalent to 453.59 g.
Now, to solve by using cross multiplication method:
By cross multiplying we get:
Dividing both sides by 200 we get:
The quantity of milk = 272.154 ml.
Now, converting the quantity into cups by conversion factor:
1 ml = 0.004 cup.
So, 272.154 ml of milk is:
272.154 × 0.004
=1.088 cups.
Estimating the number = 1 cup.
Therefore, 1 cup of milk Juan should use.