Question

Please explain steps to solve

Answer 1

Explanation:

use formula to find hypotenuse

`\sqrt{ {(a)}^(2) } + {(b)}^(2) = c`

it will be

square root (11)² + (5)² = c

square root 121 + 25 = c

square root 146 = c

12.08 = c

LM = 12.08

Answer 2

11

Explanation:

To find LM we need PM. We can use the Pythagorean Theorem:

• a^2+b^2=c^2
• PN^2+PM^2=MN^2
• 5^2+PM^2=11^2
• 25+PM^2=121
• PM^2=96
• PM=√96

Now using the Pythagorean Theorem, we can find LM:

• a^2+b^2=c^2
• LP^2+PM^2=LM^2
• 5^2+(√96)^2=LM^2
• 25+96=LM^2
• 121=LM^2
• 11=LM

Or you could have seen that triangle LPM is congruent to triangle NPM by SAS (5, 90º, and PM) so LM=NM=11.