Question

In right angled triangle ABC, Perimeter =12cm Area = 6cm. Find length of each side​

Answer 1

Answer:

Let X and Y be the legs and Z be the hypotenuse.

X^2 + Y^2 = Z^2(equation 1)

1/2×X×Y = 6, Y = 12/X(equation 2)

X + Y + Z = 12, Z = 12 - (X + Y)(equation 3)

Substituting the second and third equation in first equation, we get

X^2 + (12/X)2 = (12 - (X + 12/X))^2

X^2 + 144/X^2 = (12 -(X^2 + 12)/X)^2

(X^4 + 144)/X^2 = ((12X -X^2 -12)/X)^2

(X^4 + 144)/X^2 = (12X - X^2 -12)^2/X^2

X^4 +144 = 144X^2 + X^4 + 144 -24X^3 -288X +24X^2

-24X^3 + 168X^2 -288X = 0

24X^3 -168X^2 + 288X = 0

X^3 - 7X^2 + 12X = 0, X(X^2 -7X +12) = 0

X×(X - 4)×(X - 3) = 0, X = 4, Y = 3

Using pythagoras theorem Z = 5

So the two legs of right triangle are 4 and 3, hypotenuse is 5.