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
Y = 90 and Z = 75 , So 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 QPR an angle of 75 .
Step 3 : Draw PQS an angle of 15
Step 4 : Now we bisect QPR and 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 Y = 90 and Z = 75 , So X = 15 and XY + YZ + XZ = 11.5 cm (Ans)
![](https://s3mn.mnimgs.com/img/shared/ck-files/ck_56e57475f04be.jpg)
Hope this information will clear your doubts about Constructions .
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards
Please find below the solution to the asked query:
Given : Perimeter of triangle = 11.5 cm
And
Y = 90 and Z = 75 , So 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 QPR an angle of 75 .
Step 3 : Draw PQS an angle of 15
Step 4 : Now we bisect QPR and 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 Y = 90 and Z = 75 , So X = 15 and XY + YZ + XZ = 11.5 cm (Ans)
![](https://s3mn.mnimgs.com/img/shared/ck-files/ck_56e57475f04be.jpg)
Hope this information will clear your doubts about Constructions .
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards