Question

A student attempted to draw a triangle with given measurements PQ = 2 cm, QR = 6 cm, PR = 3 cm. First he drew QR = 6cm. Then he drew an arc of 2cm with Q as centre and he drew another arc of radius 3 cm with R as centre. They could not intersect each to get P.
What is the reason ?
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Answer 1

$\large \underline{ \underline{{ \sf{ \bigstar \: Given \: measurements \: \bigstar}}}}$

==> PQ  =  2 cm

==> QR  =  6 cm

==> PR  =  3 cm

Step 1 :

Draw a line segment QR  =  6cm

(Here we take the longest side)

Step 2 :

With ‘R’ as centre, draw an arc of radius 3 cm above the line QR.

Step 3:

With ‘Q’ as center, draw an arc of c cm above the line QR

Step:4

Now, the arc said in step 2 and arc said in step 3 must intersect.

Let us apply the above steps and see whether the two arcs intersect. 

In the above figure, the two arcs said in step 2 and step 3 do not intersect. 

Since the two arcs do not intersect, we can not draw a triangle with the given the three sides. 

$\large \underline{ \underline {\sf { \bigstar \: Reason \: \bigstar}}}$

According to the property of triangles, we have that he sum of any two sides of a triangle is always greater than the third side.

But here, the sum of the two sides 2 and 3 is less than the third side 6.

Answer 2

Answer:

According to the property of triangles, we have that he sum of any two sides of a triangle is always greater than the third side.

But here, the sum of the two sides 2 and 3 is less than the third side 6.

Step-by-step explanation: