Question

Identifying Lengths of the Sides of a Right Triangle.

Answer 1

Answer:

The side lengths of a right triangle among the given options are

1. 3, 14, and square root 205
2. 2, 9, and square root 85

Solution:

Let us assume that the three sides of a right triangle are a, b and c

So as per Pythagoras theorem, we know,

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

Here for 3, 14, and square root 205,

$(\sqrt{205})^{2}=205$

$3^{2}+14^{2}=9+196=205$

So this satisfies the right triangle

For 6,11, and square root 158

$(\sqrt{158})^{2}=158$

$6^{2}+11^{2}=157$

So this do not satisfy the right triangle

For 19, 180, and 181

$(\sqrt{181})^{2}=181$

$19^{2}+180^{2}=32400$

So this do not satisfy the right triangle

Again for 3, 19, and square root 380

$(\sqrt{380})^{2}=380$

$3^{2}+19^{2}=9+361=370$

So this do not satisfy the right triangle

For 2, 9, and square root 85

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

$2^{2}+9^{2}=85$

So, this satisfies the right triangle .

Answer 2

Answer:

not sure. I got the numbers right, but right angle no

Step-by-step explanation: