Respuesta :
Answer:
3, 14, and StartRoot 205 EndRoot
19, 180, and 181
2, 9, and StartRoot 85 EndRoot
Step-by-step explanation:
we know that
In a right triangle, the length sides must satisfy the Pythagorean Theorem
so
[tex]c^2=a^2+b^2[/tex]
where
c is the greater side (the hypotenuse)
a and b are the legs
Part 1) we have
3, 14, and StartRoot 205 EndRoot
we have
[tex]c=\sqrt{205}\ units[/tex]
[tex]a=3\ units\\b=14\ units[/tex]
substitute
[tex](\sqrt{205})^2=3^2+14^2[/tex]
[tex]205=205[/tex] ----> is true
Satisfy the Pythagorean theorem
therefore
These are the lengths of a right triangle
Part 2) we have
6, 11, and StartRoot 158 EndRoot
we have
[tex]c=\sqrt{158}\ units[/tex]
[tex]a=6\ units\\b=11\ units[/tex]
substitute
[tex](\sqrt{158})^2=6^2+11^2[/tex]
[tex]158=157[/tex] ----> is not true
Not satisfy the Pythagorean theorem
therefore
These are not the lengths of a right triangle
Part 3) we have
19, 180, and 181
we have
[tex]c=181\ units[/tex]
[tex]a=19\ units\\b=180\ units[/tex]
substitute
[tex]181^2=19^2+180^2[/tex]
[tex]32,761=32,761[/tex] ----> is true
Satisfy the Pythagorean theorem
therefore
These are the lengths of a right triangle
Part 4) we have
3, 19, and StartRoot 380 EndRoot
we have
[tex]c=\sqrt{380}\ units[/tex]
[tex]a=3\ units\\b=19\ units[/tex]
substitute
[tex](\sqrt{380})^2=3^2+19^2[/tex]
[tex]380=370[/tex] ----> is not true
Not satisfy the Pythagorean theorem
therefore
These are not the lengths of a right triangle
Part 5) we have
2, 9, and StartRoot 85 EndRoot
we have
[tex]c=\sqrt{85}\ units[/tex]
[tex]a=2\ units\\b=9\ units[/tex]
substitute
[tex](\sqrt{85})^2=2^2+9^2[/tex]
[tex]85=85[/tex] ----> is true
Satisfy the Pythagorean theorem
therefore
These are the lengths of a right triangle
