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Question

Construct a triangle ABC in which BC=7cm,B=75 and AB+AC=13 cm

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Solution

Given:
In ABC,BC=7cm,B=75 and AB+AC=13cm

Method 1:

Steps of construction:
1.Draw the base BC=7cm
2.At the point B first make an angle of 90 and then bisect the angle between 90 and 60 to get XBC=75 (As shown in the figure)
3.Cut a line segment BD equal to AB+AC=13cm from the ray BX
4.Join DC
5. Now, draw a perpendicular bisector of line CD with the help of a compass.
6. Let that perpendicular bisector intersect line BD at point A

7. Join AC.

Thus, ABC has been constructed.



Method 2:

Steps of construction:

i) Draw a base BC=7 cm.

ii) Make CBX measuring 75 using a protractor.

iii) With B as center and radius equal to 13 cm, draw an arc to intersect ray BX at D.

iv) Join DC.

v) Measure D and make ACD=D. [Since sides opposite to equal angles are equal, AC=AD.]

vi) Let CY intersect BD at A.

ABC is the required triangle.



Verification:

We see that,

BC=7 cm,B=75 and AB+AC=13 cm.


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