Question

let ABC be a triangle such that AB = (x-1)cm,AC=2√x cm,BC=(x+1) cm.then

(a) A=90 degree
(b) B=90degree
(c) C=90degree
(d) none of these
​

Answer 1

Answer:

B=90 degree this option is correct

Answer 2

Option A : Angle A is the right angle in the given triangle i.e. A = 90 degrees.

Given :

Length of side AB = $x -1$

Length of side AC = $2\sqrt{x}$

Length of side BC = $x +1$

To Find :

The right angle in triangle ABC

Solution :

Ways to find a right angle in a right-angled triangle :

1. Pythagoras theorem: The sum of squares of two sides is equal to the square of the third side according to this theorem. The angle between the sides that sum up is a right angle.
2. The angle opposite to the hypotenuse i.e. the longest side in the triangle is a right angle.

Here, we first find the squares of all the sides of the triangle :

$(AB)^{2} = (x-1)^{2}$

          $= x^{2} -2x +1$

$(AC)^{2} = (2\sqrt{x} )^{2}$

          $= 4x$

$(BC)^{2} = (x+1)^{2}$

          $= x^{2} +2x +1$

Summing up the squares of two smaller sides i.e. AB and AC :

                  $(AB)^{2} + (AC)^{2} = (x^{2} -2x+1) + (4x)$

                                           $=x^{2} - 2x + 4x +1$

                                           $= x^{2} +2x+1$

                                           $= (x+1)^{2}$

                                           $= (BC)^{2}$

Thus, the sum of squares of side AB and AC equals the square of BC. Hence, BC is the hypotenuse, and the angle opposite to it i.e. A is the right angle.

Hence, Angle A is right-angled i.e. 90 degrees.

To learn more about Pythagoras Theorem, visit

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