The length, in cm, of the sides of a right angled triangl...
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
4
5
13
17
Correct answer is B
(x+2)2=x2+(x+1)2
x2+4x+4=x2+x2+2x+1
2x2−x2+2x−4x+1−4=0
x2−2x−3=0
x2−3x+x−3=0⟹x(x−3)+1(x−3)=0
(x−3)(x+1)=0⟹x = 3 or -1
x>0⟹x=3
The longest side = 3 + 2 = 5.