Question

do you agree with the statement triangle xyz can be constructed if y=90,z=75 and xy+yz+zx=11.5 cm.why/why not?

Answer 1

I agree. It is possible to construct the triangle  xyz.  As the angles are given, we can make a triangle of any size we want.  When the perimeter is given, there exists only one triangle with given angles and given perimeter.
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∠x = 90°     ∠y = 75°     So ∠z = 15°
Pythagoras theorem:  xz² = xy² + yz²

Given  xy + yz + zx = 11.5 cm
    xy = zx Sin z = zx Sin 75°
    yz = zx cos z = zx Cos 75°

So   zx (1+ Sin 75° + cos 75°) = 11.5 cm
       zx = 5.169 cm
       xy = 4.993 cm