Determine whether each set of side lengths could be the sides of a right triangle. Drag and drop each set of side lengths to the
1 answer:
Answer:
- Right Triangle-10.5 cm, 20.8 cm, 23.3 cm
- Not a Right Triangle-6 cm, 22.9 cm, 20.1 cm
Step-by-step explanation:
Given the sets of side lengths of a triangle:
- 10.5 cm, 20.8 cm, 23.3 cm
- 6 cm, 22.9 cm, 20.1 cm
To verify whether each set of side lengths could be the sides of a right triangle, we use the Pythagorean Theorem. Note that the longest side is always taken as the hypotenuse.
- Pythagoras Theorem:
In the set of side lengths 10.5 cm, 20.8 cm, 23.3 cm
Clearly these satisfies the required theorem and thus are side lengths of a right triangle.
In the set of side lengths 6 cm, 22.9 cm, 20.1 cm
Clearly these does not satisfy the required theorem and thus are not side lengths of a right triangle.
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Answer:
(x, y, z) = (3, -2, 4)
Step-by-step explanation:
The attachment shows a solution using a graphing calculator where the first equation is solved for z, and that expression is substituted into each of the other two equations. The solution to that system is (x, y) = (3, -2). Using these values in the expression for z, we find ...
z = 5 -(3 +(-2)) = 4
The solution is (x, y, z) = (3, -2, 4).
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Your graphing calculator and/or online tools can give you the reduced row echelon form of the augmented matrix representing the system:
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If you're solving by hand, you can do the substitution described above to eliminate z from one equation. You can eliminate z from another equation by adding the last two:
-3x -4y +4(5 -x -y) = 15 ⇒ -7x -8y = -5
(-3x -4y +4z) +(2x -y -4z) = (15) +(-8) ⇒ -x -5y = 7
This pair of equations can be solved for x and y in any of the usual ways. Using the second equation to substitute for x, for example, gives you ...
-7(-5y -7) -8y = -5 ⇒ 27y = -54 ⇒ y = -2
x = -5(-2) -7 = 3
z = 5 -(3) -(-2) = 4
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<em>Additional comment</em>
If all that is needed is a solution, we prefer a graphical or matrix approach. These take about the same amount of time. Both require a little additional effort to determine exact values when the solutions are not integers.
