Question

constust a triangle xyz in which y = 30° z=90°
xy + yz + zx = 17 cm

Answer 1

1) Draw a base of 17 cm.

2) Draw bisectors of the angles given.Here,you need to draw 30°/2 = 15° and 90°/2 =45° from the ends of the segment.

3) Elongate them till they meet at a point. Say, this point is X.

4) Draw perpendicular bisectors for both the sides. 

5) Elongate both the perpendicular bisectors till they meet at the base. These are points Y and Z.

6) Join Y and Z to X.

7) ∆XYZ is complete.

Yay! We completed the construction. Recheck it by measuring the angles and the perimeter. :D

Answer 2

construction steps : 
1. Draw the base line let it be AB = 17 cm 
2. now from point A draw a angle of 30°
3. now from point B draw a angle of 90°
4. now bisect the angle A i.e. 30 / 2 = 15° and it would be ray Ax
5. now bisect the angle B i.e. 90 / 2 = 45° and it would be ray Bx
6. here we will extent the ray so that it will meet at one point. that point is the point x 
7. now draw perpendicular bisector for the ray Ax and Bx 
8. now we need to extent the bisectors towards the base line. 
9. the points where the perpendicular bisectors meet at base line will be y and z 
10. now when we measure xy + yz + zx = 17cm  
∴ the required triangle is constructed.