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Mr. Carpenter is building a treehouse . He needs to begin with part of the structure in the shape of a right triangle . He has several different lengths of wood to choose from , as listed below . Determine which of the options would form a right triangle .A. 9 meters , 7 meters , and 6 metersB. 12 meters , 10 meters , and 8 meters C. 16 meters , 10 meters , and 12 meters D. 20 meters , 21 meters , and 29 meters

Respuesta :

We need to use the Pythagorean theorem

[tex]c^2=a^2+b^2[/tex]

c is always the bigger side, if the sum of the square of the other sides is c^2 then we have a right triangle

for 9m , 7m, 6m

[tex]a^2+b^2=7^2+6^2=85[/tex][tex]c^2=9^2=81[/tex]

[tex]81\ne85[/tex]

it is not a right triangle

for 12m, 10m, 8m

[tex]a^2+b^2=10^2+8^2=164[/tex][tex]c^2=12^2=144[/tex][tex]144\ne164[/tex]

it is not a right triangle

for 16m,10 m,12m

[tex]a^2+b^2=10^2+12^2=244[/tex]

[tex]c^2=16^2=256[/tex][tex]256\ne244[/tex]

it is not a right triangle

for 20m, 21m, 29m

[tex]a^2+b^2=20^2+21^2=841[/tex]

[tex]c^2=29^2=841[/tex][tex]841=841[/tex]

It is a right triangle

the correct answer is D.

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