if three sides of a right angled triangle is given by (x+3)cm,(x+1)cm and 2xcm as the hypotenuse find the value of x

Answer 1

Pythagorean theorem:

( x + 3 )² + ( x + 1 )² = ( 2 x )²

x² + 2 ∙ x ∙ 3 + 3² + x² + 2 ∙ x ∙ 1 + 1² = 4 x²

x² + 6 x + 9 + x² + 2 x + 1 = 4 x²

2 x² + 8 x + 10 = 4 x²

Subtract 4 x² to both sides

2 x² + 8 x + 10 - 4 x² = 4 x² - 4 x²

- 2 x² + 8 x + 10 = 0

Divide both sides by - 2

x² - 4 x - 5 = 0

The solutions are x = 5 and x = - 1

Length cannot be negative so x = 5

Proof:

( x + 3 )² + ( x + 1 )² = ( 2 x )²

( 5 + 3 )² + ( 5 + 1 )² = ( 2 ∙ 5 )²

8² + 6² = 10²

64 + 36 = 100

100 = 100