Construct an isosceles triangle XYZ in which base YZ = 5.8 cm and altitude from X on YZ is 3.8 cm.

Here, we are supposed to construct an isosceles triangle XYZ, with base YZ and altitude from X on YZ given.

Steps of construction will be:

1. Draw a line segment sufficiently long using a ruler.

2. Locate points Y and Z on the line such that YZ = 5.8 cm.

3. Draw a perpendicular bisector of YZ.

For this, fix your compass at approximately more than the length of YZ and make a circle or semicircle, or two arcs taking Y as centre on either sides of the line YZ, then similarly make two more arcs taking Z as centre cutting the previous arcs. Join the two intersections and call it MP with M on YZ.

4. With M as centre and radius 3.8 cm, draw an arc cutting MP at X using a compass.

5. Join XY and XZ.

Thus, XYZ is the required triangle.