Justify whether triangle XYZ can be constructed if angle Y=90 degrees, z=75 degrees and XY+YZ+XZ=11.5

Dear Student,

Please find below the solution to the asked query:

Given :   Perimeter of triangle = 11.5 cm
And
$\angle$  Y = 90$°$ and $\angle$ Z = 75$°$ , So $\angle$ X  =  15$°$

To construct required triangle there are steps of construction :

Step 1 : Draw PQ as length of the perimeter = 11.5 cm

Step 2 : Draw $\angle$ QPR an angle of  75$°$  .

Step 3 : Draw $\angle$ PQS an angle of  15$°$

Step 4 : Now  we bisect $\angle$ QPR  and $\angle$ PQS  bisector , these meet at point Y.

Step 5 : Draw  perpendicular bisector : LM perpendicular bisector of PY and NO is perpendicular bisector of QY .

Step 6 : Line LM intersect line PQ at Z and line NO intersect line PQ at X .

Step 7 : Join XY and ZY

Then form triangle XYZ is our required triangle , Here $\angle$  Y = 90$°$ and $\angle$ Z = 75$°$ , So $\angle$ X  =  15$°$ and XY +  YZ  + XZ  =  11.5 cm                 (Ans)


                           

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