Q. 14.4( 25 Votes )

# Construct a

Answer :

We are given with perimeter of triangle and ratio of its sides. We need to construct a triangle using the given information.

Steps of construction:

1. Draw a line segment using ruler and locate points X and Y such that XY = 13 cm. 2. Draw a ray XZ, making an acute angle with XY and drawn in the downward direction. An acute angle is an angle less than right angle (less than 90°). Use the protractor to measure the acute angle. Here, YXZ < 90° obviously.

3. From X, locate (3 + 4 + 5) = 12 points at equal distances along XZ. 4. Mark points L, M, N on XZ such that XL = 3 parts, LM = 4 parts and MN = 5 parts. 5. Now, join NY. Through L and M, draw LB NY and MC NY, intersecting XY at B and C respectively. 6. With B as centre and BX as radius, draw a circle or semicircle or an arc.

Keep one end of compass fixed at B and then draw a fine circle or arc with it. 7. With C as centre and CY as radius, draw another circle or semicircle or arc cutting the previous arc at A.

Keep one end of the compass fixed at C, and then draw a fine circle or arc with it. 8. Finally, join AB and AC. Thus, ABC is the required triangle.

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