Question

Sushanth prepared a problem. Construct ΔXYZ in which XY = 2 cm, YZ = 8 cm and XZ = 4 cm. He also draw the , rough sketch as shown in figure (i).

(i)

Reading the problem, Srija told Sushanth that it would not be possible to draw a triangle with the given measurements. However, Sushanth started to draw the diagram as shown in figure (ii).Check whether Sushanth can draw the triangle. If not, why ? Discuss with your firends. What property of triangles supports Srija’s idea ?

(ii)

Answer 1

XY = 2 cm, YZ = 8 cm, XZ = 4 cm 

Sushanth can not draw the triangle. This is because, in a triangle, the sum of any two sides of a triangle is greater than its third side. But in this case, sum of the two sides is not greater than the third side. 

That is XY + XZ ≯ YZ 

2 + 4 ≯ YZ

So, it is not possible to construct a triangle with the given measurements.