Question

2$
1. In a right triangle. the length of the hypot-
enuse is 2 cm more than the length of the
base and 1 cm more than twice the length of
the altitude. Find the length of the hypot-
enuse.​

Answer 1

Answer:

Let the hypotenuse of the triangle be xcm

Let the base of the triangle be ycm

Let the altitude of the triangle be zcm

According to the given equation

x=y+2  and x=2z+1

y=x−2 and z=2x−1

Applying Pythagoras theorem 

(AC)2=(AB)2+(BC)2

x2=y2+z2

⇒x2=(x−2)2+(2x−1)2 

⇒x2=44(x−2)2+(x−1)2

⇒4x2=4(x2+4−4x)+x2+1−2x

⇒4x2=4x2+16−16x+x2+1−2x

⇒x2−18x+17=0

⇒x2−17x−x+