Question

Which are the side lengths of a right triangle? Check all that apply.

Answer 1

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

$c^2=a^2+b^2$

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

$c=\sqrt{205}\ units$

$a=3\ units\\b=14\ units$

substitute

$(\sqrt{205})^2=3^2+14^2$

$205=205$ ----> 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

$c=\sqrt{158}\ units$

$a=6\ units\\b=11\ units$

substitute

$(\sqrt{158})^2=6^2+11^2$

$158=157$ ----> 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

$c=181\ units$

$a=19\ units\\b=180\ units$

substitute

$181^2=19^2+180^2$

$32,761=32,761$ ----> 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

$c=\sqrt{380}\ units$

$a=3\ units\\b=19\ units$

substitute

$(\sqrt{380})^2=3^2+19^2$

$380=370$ ----> 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

$c=\sqrt{85}\ units$

$a=2\ units\\b=9\ units$

substitute

$(\sqrt{85})^2=2^2+9^2$

$85=85$ ----> is true

Satisfy the Pythagorean theorem

therefore

These are the lengths of a right triangle

Answer 2

Answer:  I think it's C. Ur welcome..