Question

the length of the hypotenuse of a right Triangle exceed the length of its base by 1 cm and exceeds twice the length of the altitude by 3 cm find the length of each side of the triangle.

Answer 1

base = x
hypotenuse = (x + 1)
2 x altitude + 3 = x + 1
2 x altitude = x + 1 - 3
= x - 2
altitude = (x -2) /2
xA /q
2
x. + 4 + 2x. 2. 2
------------------- + x. = x. +1 + x
4
2. 2. 2
x. +4. +2x + 4x. = 4( x. +1 +x)
2. 2
5x. +4 +2x = 4x. +4 +4x
2. 2
5x. - 4x. = 4 + 4x -4 -2x
2
x. = 2x
2
x. - 2x = 0
x(x - 2) = 0
x - 2 = 0/x
x-2 =0
x = 0+2
x = 2

Base = 2 cm.
Hypotenuse = 2+1
= 3cm.
Altitude =(2-2) /2
= 0/2
= 0 cm.
(Wrong Question)