The length, in cm, of the sides of a right angled triangle are x, (x+2) and (x+1) where x > 0. Find , in cm, the length of its hypotenuse
-
A.
4 -
B.
5 -
C.
13 -
D.
17
Correct Answer: Option B
Explanation
The longest side of a right angle triangle is the hypotenuse.
((x + 2)^{2} = x^{2} + (x + 1)^{2})
(x^2 + 4x + 4 = x^2 + x^2 + 2x + 1)
(2x^{2} – x^{2} + 2x – 4x + 1 – 4 = 0)
(x^{2} – 2x – 3 = 0)
(x^{2} – 3x + x – 3 = 0 implies x(x – 3) + 1(x – 3) = 0)
((x – 3)(x + 1) = 0 implies text{x = 3 or -1})
(x > 0 implies x = 3)
The longest side = 3 + 2 = 5.