Question

Sam wishes to fit three rods together in the shape of a right triangle ,the hypotenuse is to be 1 cm longer than the base and 8cm longer than the altitude. what should be the length of the rods

Answer 1

let the base be x
So , hypotenuse = X+1

Altitude will be (x+1)-(8)
= x-7

u can use phythogoras theorem to find x

Answer 2

the hypotenuse be x
the base is x-1
the attitude equal to other side so,
attitude is x-8
Pythagoras therom,
(digonal)2=(side)2+(side)2
(x)2=(x-1)2+(x-8)2
(x)2=(x)2+(1)2-2x+(x)2+(8)2-16x
(x)2=2x2+65-18x
(x)2-2x2=65-18x
-x2=65-18x
65-18x+x2=0
x2-13x-5x+65=0
x(x-13)-5(x-13)
(x-13)(x-5)
x=13 or x=5
the length of the road is
x=13. or. x=5.
x-1=12. x-1=4.
x-8=5. x-8=-3.
the length will not come in negative number so,
x=13
x-1=12
x-8=5