Question

Which are right triangles and which are not?There are 4 triangles.(0.9, 1.2,and 1.5)(7, 10, and 15)(3.1, 5.7,and 7.1)(1, 2.4, and 2.6) .

Answer 1

Only `(0.9,1.2,1.5)` is a right angled trangle.

Explanation:

Let these triangles be `DeltaA-(0.9,1.2,1.5)`; `DeltaB-(7,10,15)`; `DeltaC-(3.1,5.7,7.1)` and `DeltaD-(1,2.4,2.6)`

In a right angled triangle, we should have

sum of the squares of smaller two sides should be equal to the square on the largest side.

In `DeltaA`, we have `0.9^2+1.2^2=0.81+1.44=2.25` and `1.5^2-2.25` - hence `DeltaA` is right angled triangle .

In `DeltaB`, we have `7^2+10^2=49+100=149` and `15^2=225` - hence `DeltaA` is not a right angled triangle. In fact as `149 < 225`, it is an acute angled triangle.

In `DeltaC`, we have `3.1^2+5.7^2=9.61+32.49=42.10` and `7.1^2=50.41` - hence `DeltaC` is not a right angled triangle and as `42.10 < 50.41`, it is an acute angled triangle.

In `DeltaD`, we have `1.2^2+2.4^2=1.44+5.76=7.20` and `2.6^2=6.76` - hence `DeltaD` is not a right angled triangle. In fact as `7.20 > 6.76`, it is an obtuse angled triangle.