In a triangle, if the sum of two sides is x and their product is y such that (x+ z) (x-z)=y, where z is the third side of the triangle, then the triangle is

Correct Answer is : Obtuse angled

NIMCET 2021 Question Paper with solutions

Question : 50 of 120

Marks: +1, -0

In a triangle, if the sum of two sides is

x

and their product is

y

such that

(x+

(x-z)=y

, where

z

is the third side of the triangle, then the triangle is

Solution:

Let the sides be

a, b\ \&\ c

Then,

x=a+b

\& \ y=a b, \ \&\ z=c

According to the question,

(x-z)(z+x)=y

⇒ x^{2}-z^{2}=y

⇒(a+b)^{2}-c^{2}=a b

⇒ a^{2}+b^{2}+2 a b-c^{2}=a b

⇒ a^{2}+b^{2}-c^{2}=-a b

⇒{a^{2}+b^{2}-c^{2}}/{a b}=-1

⇒{a^{2}+b^{2}-c^{2}}/{2 a b}={-1}/{2}

⇒ \cos c={-1}/{2}

⇒∠ C={2 \π}/{3}

Obtuse angled triangle.

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