Question

Use the Pythagorean theorem to determine which of the following give the measures of the legs and hypotenuse of a right triangle: 3, 4, 5 or 4, 11, 14 or 9, 14, 17 or 8, 14, 16 or 8, 15, 17.

Answer 1

longest side =5
it's square =25......(1)
sum of remaning two sides
= 3² + 4²
= 9 + 16
=25........(2)
from (1) and (2)
5²= 3²+4²
therefore by converse of Pythagoras Theorem it is a right angled triangle.

longest side =14
it's square =196......(1)
sum of remaning two sides
= 4² + 11²
= 16 + 121
=277........(2)
from (1) and (2)
14² ≠ 4²+11²
therefore by converse of Pythagoras Theorem it is not a right angled triangle.

longest side =17
it's square =289......(1)
sum of remaning two sides
= 9² + 14²
= 81 + 196
=277........(2)
from (1) and (2)
17² ≠ 9² + 14²
therefore by converse of Pythagoras Theorem it is not a right angled triangle.


longest side =16
it's square =256......(1)
sum of remaning two sides
= 8² + 14²
= 64 + 196
=260........(2)
from (1) and (2)
16² ≠8² + 14²
therefore by converse of Pythagoras Theorem it is not a right angled triangle.

longest side =17
it's square =289......(1)
sum of remaning two sides
= 8² + 15²
= 64 + 225
=289........(2)
from (1) and (2)
17²= 8²+15²
therefore by converse of Pythagoras Theorem it is a right angled triangle.