Question

listed below are the side lengths of right triangles. Identify each triangle with a missing side that is equivalent to 12 in

Answer 1

If the missing side is 12in the sides must satisfy the Pythagorean theorem

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

For the first option, we have 8in,12in,17 in

where

a=8in

b=12in

c=17 in

`a^2+b^2=8^2+12^2=208`
`c^2=17^2=289`

the results are different therefore it is not a right triangle with a missing side of 12.

For the second option, we have 12in, 20in,25in

a=12 in

b=20 in

c=25 in

`a^2+b^2=12^2+20^2=544`
`c^2=25^2=625`

the results are different therefore it is not a right triangle with a missing side of 12.

For the third option, we have 5in, 12in, 13in

a=5 in

b=12 in

c=13 in

`a^2+b^2=5^2+12^2=169`
`c^2=13^2=169`

It is a right triangle with a missing side of 12 in

For the fourth option, we have 9in, 12 in 15 in

a=9in

b=12in

c=15 in

`a^2+b^2=9^2+12^2=225`
`c^2=15^2=225`

It is a right triangle with a missing side of 12 in

For the fifth option, we have 12in ,60in, 61in

a=12in

b=60in

c=61in

`a^2+b^2=12^2+60^2=3744`
`c^2=61^2=3721`

the results are different therefore it is not a right triangle with a missing side of 12.

For the sixth option we have 12 in, 35 in, 37 in

a=12in

b=35 in

c=37 in

`a^2+b^2=12^2+35^2=1369`
`c^2=37=1369`

It is a right triangle with a missing side of 12 in