Question

Construct ΔXYZ, such that YZ = 7.4 cm, ∠XYZ = 45° and XY - XZ = 2.7 cm.

Answer 1

Rough figure:

Explanation:

Here, XY – XZ = 2.7 cm

∴ XY > XZ

As shown in the rough figure draw seg YZ = 7.4 cm

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

Take a point W on ray YP, such that

YW = 2.7 cm.

Now, XY – XW = YW     ...[Y-W-X]

∴ XY – XW = 2.7 cm     ...(i)

Also, XY – XZ = 2.7 cm      ...(ii) [Given]

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

∴ XW = XZ

∴ Point X is on the perpendicular bisector of seg ZW.

∴ Point X is the intersection of ray YP and the perpendicular bisector seg ZW.

Steps of construction:

1. Draw seg YZ of length 7.4 cm.
2. Draw ray YP, such that ∠ZYP = 45°.
3. Mark point W on ray YP such that l(YW) = 2.7 cm.
4. Join points W and Z.
5. Join the points X and Z.

Therefore, △XYZ is required triangle.