Answer:
Based on the converse of the Pythagorean Theorem, the triangle is not a right triangle, because [tex]9+12\neq 15[/tex]
Step-by-step explanation:
The complete question in the attached figure
we know that
If the length sides of a triangle, satisfy the Pythagorean Theorem, then is a right triangle
[tex]c^2=a^2+b^2[/tex]
where
c is the hypotenuse (the greater side)
a and b are the legs
In this problem
The length sides squared of the triangle are equal to the areas of the squares
so
[tex]c^2=15\ in^2[/tex]
[tex]a^2=12\ in^2[/tex]
[tex]b^2=9\ in^2[/tex]
substitute
[tex]15=12+9[/tex]
[tex]15=21[/tex] ----> is not true
so
The length sides not satisfy the Pythagorean Theorem
therefore
Based on the converse of the Pythagorean Theorem, the triangle is not a right triangle, because [tex]9+12\neq 15[/tex]
