Question

3. In AABC, LA
BC = 135º, prove that
AC2 = AB? + BC? + 4A(AABC)​

Answer 1

Answer:

produce CB to D such that AD becomes its perpendicular.

Now triangle ABC is a triangle obtuse angled at B.

So by obtuse angled theorem we have,

AC2= AB2+ BC2+ 2 BC.BD ............ (1)

As it is told that angle ABC is 1350. So angle ABD will be 180 - 135 = 450.

Now angle ADB is of 90 degrees and angle ABD is of 45 degrees. So angle DAB will be 45 degrees

Now triangle ADB is an isosceles triangle because its two angles DAB and ABD is 45 degrees. So AD = DB.

Replacing BD with AD in equation (1), we have

AC2= AB2+ BC2+ 2 BC.AD

AC2= AB2+ BC2+ 4 * 1/2 BC.AD

AC2= AB2+ BC2+ 4 (ar ABC)