The lengths of the adjacent sides of a right - angled triangle are xcm, (x-1)cm. If the length of the hypotenuse is \(\sqrt{13}cm\), find the value of x
A
2
B
3
C
4
D
5
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
Using Pythagoras' theorem
\(x^2+(x-1)^2 = (\sqrt{13})^2\)
x\(^2\) + x\(^2\) - 2x + 1 = 13
2x\(^2 - 2x\) - 12 = 0
dividing through by 2
x\(^2\) - x- 6 = 0; (x-3)(x-2) = 0
x = 3 or -2
Source: Myschool Past Questions Archive (Record #26684)