Answers for problem 2
- (a) Right triangle
- (b) Right triangle
- (c) Right triangle
- (d) NOT a Right triangle
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Work Shown for Problem 2, part (a)
The sides of the triangle are: a = 9, b = 40, c = 41
If we had a right triangle, then a^2+b^2 = c^2 must be the case. This is the pythagorean theorem. Keep in mind that c is always the longest side known as the hypotenuse. The order of "a" and b doesn't matter.
So,
a^2+b^2 = c^2
9^2+40^2 = 41^2
81+1600 = 1681
1681 = 1681
We arrive at a true equation at the end. Therefore a^2+b^2 = c^2 is true when (a,b,c) = (9,40,41).
It confirms we have a right triangle.
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Work Shown for Problem 2, part (b)
a^2 + b^2 = c^2
10^2 + 24^2 = 26^2
100 + 576 = 676
676 = 676
The last equation is true, so a^2 + b^2 = c^2 is true for (a,b,c) = (10,24,26).
This is a right triangle.
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Work Shown for Problem 2, part (c)
a^2 + b^2 = c^2
10^2 + 10^2 = (sqrt(200))^2
100 + 100 = 200
200 = 200
This is also a right triangle.
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Work Shown for Problem 2, part (d)
a^2 + b^2 = c^2
7.5^2 + 8.3^2 = 11.2^2
56.25 + 68.89 = 125.44
125.14 = 125.44
The last equation is false, so a^2 + b^2 = c^2 is false for (a,b,c) = (7.5,8.3,11.2).
This is NOT a right triangle.
Because a^2+b^2 < c^2 is the case, we have an obtuse triangle. Search out "pythagorean theorem converse" for more information.