Question

construct ∆xyz,such that xz-xy=2.7 cm,yz=7.5cm , angle xyz=45°

Answer 1

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: (i). Draw seg YZ of length 7.4 cm. (ii). Draw ray YP, such that ∠ZYP = 45°. (iii). Mark point W on ray YP such that l(YW) = 2.7 cm. ( iv). Join points W and Z. v. Join the points X and Z. Hence, ∆XYZ is the required triangle.