Question

A triangle has side lengths of 7, 24, and 26. Is the triangle right, acute, or obtuse? a. right c. obtuse b. acute Please select the best answer from the choices provided A B C

Answer 1

Option C. Obtuse

Explanation:

we know that

Applying the Pythagoras Theorem

If
`c^(2)=a^(2) +b^(2)` ----> is a right triangle

If
`c^(2)>a^(2) +b^(2)` ----> is a obtuse triangle

If
`c^(2)<a^(2) +b^(2)` ----> is an acute triangle

where

c is the greater side

Verify

`c^(2)=26^(2)= 676`

`a^(2) +b^(2)=7^(2) +24^(2)=625`

therefore

`676>625`

`c^(2)>a^(2) +b^(2)` -----> is a obtuse triangle