Atriangular bookself has a base of 10 inches,12 inches and 18 inches. will the bookself fit in the corner of a square living room

No, if fit means that the sides of the book case need to be flush with the wall, which means that the sides of the bookcase are touching the wall and the bookcase fits perfectly in that spot

Step-by-step explanation:

A square room will have corners that meause 90°, so we need to see if any of the vertices of the bookcase measure 90°.  All right triangles have a 90° in them, so we can use Pythagorean Theorem to solve this.

 Pythagorean Theorem is  a² + b² = c²,    where a and b are the legs, and c is the hypotenuse.  Since the hypotenuse is always the longest side, for our bookshelf, 10 and 12 are the legs, and 18 would be the hypotenuse if it is a right triangle.   Plug the values in to see if the equation is true or false

10² + 12² = 18²

  100 + 144 = 324

     244 ≠ 324   so the bookcase does not form a right angle, and won't fit in the corner of the room