Question

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

Answer 1

We need to use the Pythagorean theorem

`c^2=a^2+b^2`

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

`a^2+b^2=7^2+6^2=85`
`c^2=9^2=81`

`81\\e85`

it is not a right triangle

for 12m, 10m, 8m

`a^2+b^2=10^2+8^2=164`
`c^2=12^2=144`
`144\\e164`

it is not a right triangle

for 16m,10 m,12m

`a^2+b^2=10^2+12^2=244`

`c^2=16^2=256`
`256\\e244`

it is not a right triangle

for 20m, 21m, 29m

`a^2+b^2=20^2+21^2=841`

`c^2=29^2=841`
`841=841`

It is a right triangle

the correct answer is D.