Question

In a triangle with sides of length a; b; c, suppose b + c = x and bc = y. If also (x + a)(x

a.= y, then the triangle is necessarily

Answer 1

Answer:

obtuse triangle

Step-by-step explanation:

In a triangle with sides of length a; b; c, suppose b + c = x and bc = y. If also (x + a)(x -a)= y, then the triangle is necessarily

(x + a)(x-a) = y

x² - a² = y

y = bc

x = b + c

=> (b +c)² - a² =bc

=> a² =  (b +c)² - bc

=> a² =  b² + c² + 2bc - bc

=> a² =  b² + c² + bc

we know in a given triangle

a² =  b² + c² -2bcCosA

comparing both

b² + c² -2bcCosA  = b² + c² + bc

=> -2bcCosA = bc

=> -2CosA = 1

=> cosA = -1/2

A = 120°

120° > 90°

Angle A is obtuse angle

=> triangle is obtuse triangle