The lengths of the three sides of a right-angled triangle are (x - 1)cm, (x + 1) cm and (x + 3)cm, respectively. The hypotenuse of the right-angled triangle (in cm) is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 10
According to the question,
The lengths of the three sides of a right-angled triangle are (x-1)cm, (x+1) cm and (x+3)cm
Hypotenuse is the biggest side on the triangle.
By using Pythagoras theorem
(x + 3)2 = (x - 1)2 + (x + 1)2
x2 + 6x + 9 = x2 + 1 - 2x + x2 + 1 + 2x
x2 + 6x + 9 = 2x2 + 2
x2 -6x - 7 = 0
x2 - 7x + x - 7 = 0
(x - 7) (x + 1) = 0
x = 7, and (-1) can't possible
So, hypotenuse = x + 3 = 7 + 3 = 10