Question

Construct ΔXYZ, such that XY + XZ = 10.3 cm, YZ = 4.9 cm, ∠XYZ = 45°.

Answer 1

Rough figure:

Explanation:

As shown in the rough figure draw seg YZ = 4.9 cm

Draw a ray YT making an angle of 45° with YZ

Take a point W on ray YT, such that YW = 10.3 cm

Now,YX + XW = YW     ...[Y-X-W]

∴ YX + XW = 10.3 cm      ...(i)

Also, XY + YZ = 10.3 cm     …(ii) [Given]

∴ YX + XW = XY + XZ       ...[From (i) and (ii)]

∴ XW = XZ

Point X is on the perpendicular bisector of seg WZ

∴ The point of intersection of ray YT and perpendicular bisector of seg WZ is point X.

Steps of construction: 

1. Draw seg YZ of length 4.9 cm.
2. Draw ray YT, such that ∠ZYT = 75°.
3. Mark point W on ray YT such that l(YW) = 10.3 cm.
4. Join points W and Z.
5. Draw perpendicular bisector of seg WZ intersecting ray YT. Name the point as X.
6. Join the points X and Z.

Therefore, △XYZ is the required triangle.