Question

which is the following triangles is not a right triangle? A. With the side lengths of 2.5 m, 2.0 m, and 1.5 m B. With the side lengths of 32cm, 24 cm, and 40 cm C. With the side lengths of 7cm, 14 cm, and 15 cm D. with the side lengths of 9 cm, 15 cm, and 12 cm

Answer 1

A right triangle needs to obey the Pythagora's theorem, that states:

`\text{hypothenuse}^2=\text{ side}^2_1+\text{side}^2_2`

The square of the hypothenuse is equal to the sum of the squares of the sides. The hypothenuse is the largest side of the right triangle, so we can check if this is true for each case.

a) hypothenuse = 2.5, side1 = 2 and side2=1.5

`\begin{gathered} 2.5^2=2^2+1.5^2 \\ 6.25=4+2.25 \\ 6.25=6.25 \end{gathered}`

This is a right triangle.

b) hypothenuse = 40, side1 = 32 and side2 = 24.

`\begin{gathered} 40^2=32^2+24^2 \\ 1600=1024+576 \\ 1600=1600 \end{gathered}`

This is a right triangle.

c) hypothenuse = 15, side1 = 14 and side2 = 7.

`\begin{gathered} 15^2=14^2+7^2 \\ 225=196+49 \\ 225=245 \end{gathered}`

The equation is invalid and this is not a right triangle.

d) hypothenuse = 15, side1 = 9 and side2 = 12.

`\begin{gathered} 15^2=9^2+12^2 \\ 225=81+144 \\ 225=225 \end{gathered}`

This is a right triangle.

The correct answer is "C".