Question

the hypotenuse of a right angled triangle exceeds one side by 1 cm and the other side by 18 cm find the length of the sides of the triangle

Answer 1

Let the hypotenuse be x
Let one side be x+1
Let the other side be x+18

Using  Pythagoras Property
$x^{2} = (x+1)^{2} + (x+18)^{2}$
Using Identity $(a + b)^{2} = a^{2} + b^{2} + 2ab$
$x^{2} = [x^{2} + 1^{2} + 2(x)(1)] + [ x^{2} + 18^{2} + 2(x)(18)]$
[tex] x^{2} = x^{2} + 1 +2x + x^{2} + 324 + 36x [/tex]
[tex] x^{2} - x^{2} - x^{2} = 1 + 324 + 2x + 36x [/tex]
$- x^{2} = 325 + 38x$
$x^{2} = -(325 + 38x)$
$x^{2} = -325 - 38x$