Given:
Given that a triangle has side lengths 1.5 inches, 2 inches and 3 inches.
We need to determine whether the triangle is a right triangle.
Right triangle:
To determine whether the given triangle is a right triangle, let us use the Pythagorean theorem.
Since, the value of the hypotenuse takes the largest value in the given triangle, then from the given sides, the hypotenuse is 3 inches.
The legs of the triangle are 1.5 inches and 2 inches.
Applying the Pythagorean theorem, we have;
[tex]3^2=1.5^2+2^2[/tex]
Squaring the terms, we have;
[tex]9=2.25+4[/tex]
[tex]9 \neq 6.25[/tex]
Since, both sides of the equation are not equal, then the given triangle with sides 1.5 inches, 2 inches and 3 inches is not a right triangle.
