The longest side of an isosceles right triangle measures 16m. what is the perimeter of the triangle?
A
32/2m
B
32+162m
C
16+162m
D
32+2m
Correct Answer: 16+162m
<math xmlns = "http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo> </mo><mo> + </mo><msup><mi>x</mi><mn>2</mn></msup><mo> </mo><mo> = </mo><mo> </mo><msup><mn>16</mn><mn>2</mn></msup><mspace linebreak = "newline"/><mo>⇒</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo> </mo><mo> = </mo><mn>16</mn><mo>×</mo><mn>16</mn><mspace linebreak = "newline"/><mo>⇒</mo><msup><mi>x</mi><mn>2</mn></msup><mo> </mo><mo> = </mo><mfrac><mrow><mn>16</mn><mo>×</mo><mn>16</mn></mrow><mn>2</mn></mfrac><mo> = </mo><mo> </mo><mn>8</mn><mo>×</mo><mn>16</mn><mspace linebreak = "newline"/><mo>⇒</mo><msup><mi>x</mi><mn>2</mn></msup><mo> </mo><mo> = </mo><mn>4</mn><mo>×</mo><mn>4</mn><mo>×</mo><mn>4</mn><mo>×</mo><mn>2</mn><mspace linebreak = "newline"/><mo>⇒</mo><mi>x</mi><mo> = </mo><msqrt><msup><mn>4</mn><mn>2</mn></msup></msqrt><mo> + </mo><msup><mn>2</mn><mn>2</mn></msup><mo> + </mo><mn>2</mn><mo> </mo><mo> = </mo><mn>8</mn><msqrt><mn>2</mn></msqrt></math>