In other words, if a rectangle is 10 cm by 15 cm, what is the length of the diagonal? Use the Pythagorean Theorem. a^2+b^2=c^2, where c is the measure of the hypotenuse.
A: (-3,-1)
B: (4,-5)
C: (-2,3)
D: (1,4)
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Answer:
(c) 9, 24, 26
Step-by-step explanation:
If you're familiar with Pythagorean triples, you may recognize that 10-24-26 is a doubling of the common 5-12-13 triple seen in many problems. That means the triple 9-24-26 cannot be a right triangle.
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The "form factor" of f = a^2 +b^2 -c^2, where c is the longest side length, can signal the kind of triangle it is. f=0 indicates a right triangle (values satisfy the Pythagorean theorem). When there are a lot of numbers to try, I like to let a calculator or spreadsheet do the math. (See attached).
As indicated above, the 9-24-26 triple cannot be a right triangle. For f < 0, it will be an obtuse triangle.
Answer:
29 - 6 = x
x = 23
The backpack without the sleeping bag weighs 23 pounds
Step-by-step explanation:
Sleeping bag = 6 lbs
Backpack and sleeping bag = 29