Maths-
General
Easy
Question
The sides of a right-angled triangle are 2x – 1, 2x, 2x + 1. Find x.
Hint:
Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.
If a is the perpendicular, b is the base, and c is the hypotenuse, then according to the definition, the Pythagoras Theorem formula is given as
c2= a2 + b2
The correct answer is: Hence, the value of x is 2.
In a right-angled triangle, the longest length is of the hypotenuse. So by seeing all the values we can conclude that 2x+1 will be the hypotenuse of the given right-angled triangle and the other two will be the perpendicular and base
Applying Pythagoras theorem
Hypotenuse2= Perpendicular2 + Base2
(2x + 1)2 = (2x – 1)2 + (2x)2
4x2 + 1 + 4x = 4x2 + 1 - 4x + 4x2
4x2 = 8x
x= 2
Final Answer:
Hence, the value of x is 2.
Hypotenuse2= Perpendicular2 + Base2
(2x + 1)2 = (2x – 1)2 + (2x)2
4x2 + 1 + 4x = 4x2 + 1 - 4x + 4x2
4x2 = 8x
x= 2
Final Answer:
Hence, the value of x is 2.
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