Question

The hypotenuse of a right angled triangle is 1m less than twice the shortest side. If the third side is 1m more than the shortest side , then find the sides of the triangle

Answer 1

Let a Triangle ABC ,
AC(Hypotenuse),BC(Base/shortest side),AB(Perpendicular)
ATQ,
AC=2BC-1 ----i
AB=BC+1------ii

Also

AC.AC=AB.AB+BC.BC (By Pythagoras theorem)
Putting values from I and ii
(2BC-1)(2BC-1)=(BC+1)(BC+1)+BC.BC
4BC(BC)+1-4BC=BC(BC)+1+2BC +BC.BC
4BC(BC)=2BC.BC+6BC
2BC.BC=6BC
BC=3m

HENCE,
Shortest side=3m
Hypotenuse,AC=2(3)+1=7m
Third Side,AB=(3)+1=4m

Thank you