# 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) .

Mar 20, 2017

Only $\left(0.9 , 1.2 , 1.5\right)$ is a right angled trangle.

#### Explanation:

Let these triangles be $\Delta A - \left(0.9 , 1.2 , 1.5\right)$; $\Delta B - \left(7 , 10 , 15\right)$; $\Delta C - \left(3.1 , 5.7 , 7.1\right)$ and $\Delta D - \left(1 , 2.4 , 2.6\right)$

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 $\Delta A$, we have ${0.9}^{2} + {1.2}^{2} = 0.81 + 1.44 = 2.25$ and ${1.5}^{2} - 2.25$ - hence $\Delta A$ is right angled triangle .

In $\Delta B$, we have ${7}^{2} + {10}^{2} = 49 + 100 = 149$ and ${15}^{2} = 225$ - hence $\Delta A$ is not a right angled triangle. In fact as $149 < 225$, it is an acute angled triangle.

In $\Delta C$, we have ${3.1}^{2} + {5.7}^{2} = 9.61 + 32.49 = 42.10$ and ${7.1}^{2} = 50.41$ - hence $\Delta C$ is not a right angled triangle and as $42.10 < 50.41$, it is an acute angled triangle.

In $\Delta D$, we have ${1.2}^{2} + {2.4}^{2} = 1.44 + 5.76 = 7.20$ and ${2.6}^{2} = 6.76$ - hence $\Delta D$ is not a right angled triangle. In fact as $7.20 > 6.76$, it is an obtuse angled triangle.