Question

contact triangle ABC , such that AB = 3.6 cm and BC = 5.4 cm and angle b = 60°​

Answer 1

Step-by-step explanation:

Steps of construction:

1. Draw a line segment AC = 5.4cm

2. With A as a center and radius 5cm, draw an arc.

3. With C as a center and radius 3.6cm, draw another arc, cutting the previous arc at B.

4. Join AB and CB.

Then, △ABC is the required triangle.

5. With B as center and radius measuring more than half of BC, draw arcs on both sides of BC.

6. With C as center and the same radius as before, draw arcs on both sides of BC, cutting the previous arcs at P and Q, as shown. Join PQ.

Then, PQ is the required perpendicular bisector of BC, meeting BC at M.

Answer 2

Construct a triangle ABC in which BC = 3.6 cm, AB + AC = 5.4 cm and ∠B = 60°

Steps of construction:

1. Draw a line segment AC = 5.4cm

2. With A as a center and radius 5cm, draw an arc.

3. With C as a center and radius 3.6cm, draw another arc, cutting the previous arc at B.

4. Join AB and CB.

Then, △ABC is the required triangle.

5. With B as center and radius measuring more than half of BC, draw arcs on both sides of BC.

6. With C as center and the same radius as before, draw arcs on both sides of BC, cutting the previous arcs at P and Q, as shown. Join PQ.

Then, PQ is the required perpendicular bisector of BC, meeting BC at M.

For Extra Knowledge:-

ᴛʜᴇ ᴡᴏʀᴅ “ᴍᴀᴛʜᴇᴍᴀᴛɪᴄꜱ” ɪꜱ ᴅᴇʀɪᴠᴇᴅ ꜰʀᴏᴍ ᴛʜᴇ ɢʀᴇᴇᴋ ᴡᴏʀᴅ “ᴍᴀᴛʜᴇᴍᴀ” ᴍᴇᴀɴɪɴɢ ᴋɴᴏᴡʟᴇᴅɢᴇ. ɪᴛ ɪɴᴄʟᴜᴅᴇꜱ ᴛʜᴇ ꜱᴛᴜᴅʏ ᴏꜰ ᴄᴏɴᴄᴇᴘᴛꜱ ꜱᴜᴄʜ ᴀꜱ ɴᴜᴍʙᴇʀ ᴛʜᴇᴏʀʏ, ᴀʟɢᴇʙʀᴀ, ᴍᴀᴛʜᴇᴍᴀᴛɪᴄᴀʟ ᴀɴᴀʟʏꜱɪꜱ, ᴇᴛᴄ. ᴀʀᴄʜɪᴍᴇᴅᴇꜱ ɪꜱ ᴋɴᴏᴡɴ ᴀꜱ ᴛʜᴇ ꜰᴀᴛʜᴇʀ ᴏꜰ ᴍᴀᴛʜᴇᴍᴀᴛɪᴄꜱ. ʜᴇ ʟɪᴠᴇᴅ ʙᴇᴛᴡᴇᴇɴ 287 ʙᴄ – 212 ʙᴄ. ꜱʏʀᴀᴄᴜꜱᴇ, ᴛʜᴇ ɢʀᴇᴇᴋ ɪꜱʟᴀɴᴅ ᴏꜰ ꜱɪᴄɪʟʏ ᴡᴀꜱ ʜɪꜱ ʙɪʀᴛʜᴘʟᴀᴄᴇ. ᴀʀᴄʜɪᴍᴇᴅᴇꜱ ᴡᴀꜱ ꜱᴇʀᴠɪɴɢ ᴛʜᴇ ᴋɪɴɢ ʜɪᴇʀᴏ ɪɪ ᴏꜰ ꜱʏʀᴀᴄᴜꜱᴇ ʙʏ ꜱᴏʟᴠɪɴɢ ᴍᴀᴛʜᴇᴍᴀᴛɪᴄᴀʟ ᴘʀᴏʙʟᴇᴍꜱ ᴀɴᴅ ʙʏ ᴅᴇᴠᴇʟᴏᴘɪɴɢ ɪɴᴛᴇʀᴇꜱᴛɪɴɢ ɪɴɴᴏᴠᴀᴛɪᴏɴꜱ ꜰᴏʀ ᴛʜᴇ ᴋɪɴɢ ᴀɴᴅ ʜɪꜱ ᴀʀᴍʏ.

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