Mathematics
Answer
We know that,
Sum of angles of triangle = 180°
∴ ∠L + ∠M + ∠N = 180°
⇒ ∠L + 90° + ∠N = 180°
⇒ ∠L + ∠N = 180° - 90°
⇒ ∠L + ∠N = 90°
∴ ∠M > ∠L and ∠M > ∠N.
We know that side opposite to the greatest angle is greatest side.
∴ LN is longest side of the triangle.
Hence, LN is the longest side of the triangle.
Related Questions
In the given figure, AC is the bisector of ∠A. If AB = AC, AD = CD and ∠ABC = 75°, find the values of x and y.
In a △PQR, ∠P = 50° and ∠R = 70°. Name :
(i) the shortest side
(ii) the longest side of the triangle
In the given figure, side AB of △ABC is produced to D such that BD = BC. If ∠A = 60° and ∠B = 50°, prove that :
(i) AD > CD
(ii) AD > AC
In a right angled triangle, prove that the hypotenuse is the longest side.