5" by 10" by 15" cannot be a right angled triangle because the square of the hypotenuse (longest side) must be equal to the sum of the squares of the other two sides.
Proof:
152 = 225
52 + 102 = 25 + 100 = 125
225 is not equal to 125 so the triangle is not a right angled triangle.
All the others are right-angled triangles:
92 + 122 = 152 [81 + 144 = 225]
42 + 7.52 = 8.52 [16 + 56.25 = 72.25]
1.52 + 22 = 2.52 [2.25 + 4 = 6.25]
Answer
9ft, 12ft, 15ft
9² + 12² = 81 + 144
= 225
= 15²
Which agrees with Pythagoras' Theorem, so this is a right-angled triangle.
4cm, 7.5cm, 8.5cm
4² + 7.5² = 16 + 56.25
= 72.25
= 8.5²
Which agrees with Pythagoras' Theorem, so this is a right-angled triangle.
5in, 10in, 15in
This one doesn't obey the triangle inequality, so it isn't a triangle at all. Anything that isn't a triangle isn't a right-angled triangle, and therefore we don't need to check it against Pythagoras' Theorem. But just to be thorough:
5² + 10² = 25 + 100
= 125
15² = 225
≠ 125
Which disagrees with Pythagoras' Theorem, so this is not a right-angled triangle.
1.5m, 2m, 2.5m
1.5² + 2² = 2.25 + 4
= 6.25
= 2.5²
Which agrees with Pythagoras' Theorem, so this is a right-angled triangle.
A triangle with a right angle and different lengths for sides is a right, scalene triangle.
Yes, it is.
Hypotenuse,Adjacent and opposite in a triangle and these sides can be worked out
No because the given sides do not comply with Pythagoras' theorem for a right angle triangle.
False.
A triangle with a right angle and different lengths for sides is a right, scalene triangle.
A right triangle * * * * * No, it is a scalene triangle.
162+632=652 It is, in fact, a right triangle. I see no other question that you could be posing.
A triangle with no right angle and sides of different lengths is a scalene triangle.
In Euclidean geometry, 180. Other answers are possible, depending on the surface on which the triangle is drawn.
If the lengths of the sides of the triangle can be substituted for 'a', 'b', and 'c'in the equationa2 + b2 = c2and maintain the equality, then the lengths of the sides are a Pythagorean triple, and the triangle is a right one.
Yes, it is.
True
true
Yes, it is.
If any of its 2 sides is not greater than its third in length then a triangle can't be formed.
Hypotenuse,Adjacent and opposite in a triangle and these sides can be worked out