1.

the perimeter of a right angled triangle is 70units and its hypotenus is 29 units find the length of other side​

Answer»

\large{\underline{\red{\rm{AnswEr:21\: units\:\:20\: units}}}}

\huge\bold\purple{\underline{Solution:}}

\bold\green{\underline{Given:}}

The perimeter of Triangle=70units

The hypotenous of Triangle=29 units

\bold\red{\underline{Let:}}

The other two sides be X and Y

\bold\orange{\underline{A.T.Q}}

Using, pathagoras theorem,

⟹Hypotenus²=Perpendicular²+base²

⟹29²=X²+Y²-------(1)

\bold\purple{\boxed{Perimeter\:of\: Triangle=Sum\:of\: it's\: sides}}

⟹70=X+Y+29

⟹70-29=X+Y

⟹41=X+Y---------(2)

⟹Y=41-X

Using, substituting method here

Now, putting the value of Y=41-X in EQ 1

⟹29²=X²+Y²

⟹29²=X²+(41-X)²

⟹841=X²+1681-82X+X²

⟹841=1681-82X+2X²

⟹2X²-82X+840=0

  • Dividing by 2 on both sides

⟹X²-41X+420=0

  • Splitting the middle term here

⟹X²-20X-21X+420=0

⟹X(X-20)-21(X-20)=0

⟹(X-21)(X-20)=0

Therefore, X-21=0 X=21 X-20=0 X=20

Putting the value of X=21 in EQ 2

⟹41=X+Y

⟹41=21+Y

⟹Y=41-21

⟹Y=20

Hence,

The other two sides are 21units and 20units


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