A triangular tile measures ½ ft, ¾ ft and 1 ft on its three sides. Is it a right triangle? Explain.?

Question

A triangular tile measures ½ ft, ¾ ft and 1 ft on its three sides. Is it a right triangle? Explain.

Answer 1

a^2 + b^2 > c^2 the triangle is an acute
a^2 + b^2 < c^2 the triangle is an obtuse
a^2 + b^2 = c^2 the triangle is a right triangle

(1/2)^2 + (3/4)^2 =? 1^2
1/4 + 9/16 =? 1
4/16 + 9/16 =? 1
13/16 < 1

the triangle is an obtuse

Answer 2

Change to inches, 6, 9, and 12
Pythagorian Theorem, does 6^2 + 9^2 = 12^2 ?
36 + 81 = 117, which is not 144
Therefore, not a right triangle

Note: You can work with 1,2, 3/4 and 1 if you want
(1/2)^2 + (3/4)^2 = 1/4 + 9/16, =4/16 + 9/16, =13/16,
which is not 1.

Answer 3

No, because (1/2)^2+(3/4)^2 = 1/4 + 9/16 = 4/16 +
+ 9/16 = 13/16 < 1 (The longest side's length).

Answer 4

assume it were a right triangle, then
C^2 = A^2 + B^2
since
(1/2)^2 + (3/4)^2 = 13/16
and 1^2 = 1
they are not equal, so it's not a right triangle

Answer 5

no, because by phytagoras theorem,
c^2=a^2+b^2, where c is the longest side
and since
(1/2)^2+(3/4)^2 is not equal to 1^2,
the angle is not right angled