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