Answer :

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.


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