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Question

ABC is such that AB = 5.5 cm and A = 90. Which among the given options is correct if we need to construct ABC?


A

Length of side BC < 5.5 cm

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B

Length of side BC = 5.5 cm

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C

Length of side BC > 5.5 cm

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D

Length of side BC < 5 cm

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Solution

The correct option is C

Length of side BC > 5.5 cm


Step 1:
Draw the base line AB of the length 5.5 cm.

Step 2:
Measure the angle A with your protractor. Make a mark at 90 degrees and draw a line from A passing through the mark.

Now, if we draw a circle centered at B and radius strictly less than 5.5 cm, then such a circle does not cut the line through point A. Hence triangle construction is not possible if BC < 5.5 cm.

If we draw a circle centered at B and radius equal to 5.5 cm, then such a triangle touches the line through A, at the point A. Hence triangle formation is not possible in this case too.

If we draw a circle centered at B and radius strictly greater than 5.5 cm, then such a circle intersects the line through point A at one point. This is the required point C. Then by drawing a line from point B to point C, we get a triangle.


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