If the area of a triangle is 1176 cm² and base : corresponding altitude is 3:4, then the altitude
of the triangle is:

December 16, 2021

By Charlie

2 thoughts on “<br />If the area of a triangle is 1176 cm² and base : corresponding altitude is 3:4, then the altitude<br />of the triangle is:<b”

1. Answer:

   Given :–

   Area of triangle = 1176 cm²

   Ratio of base to altitude = 3:4

   To Find :–

   Altitude

   Solution :–

   Let the base be 3x and altitude be 4x

   [tex] \sf \: 1176 = \dfrac{1}{2} \times 3x \times 4x[/tex]

   [tex] \sf \: 1176 \times 2 = 3x \times 4x[/tex]

   [tex] \sf \: 2352 = 12 {x}^{2} [/tex]

   [tex] \sf \dfrac{2352}{12} = {x}^{2} [/tex]

   [tex] \sf \:196 = {x}^{2} [/tex]

   [tex] \sf \: \sqrt{196} = \sqrt{ {x}^{2} } [/tex]

   [tex] \sf \: 14 = x[/tex]

   Altitude = 4x

   [tex] \sf \: 4 x[/tex]

   [tex] \sf \: 4(14)[/tex]

   [tex] \sf \: 56[/tex]

   Option 4

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2. [tex] \huge { \blue { \fbox{ \red{Qᴜᴇꜱᴛɪᴏɴ}}}}[/tex]

   If the area of a triangle is 1176 cm² and base : corresponding altitude is 3:4, then the altitude

   of the triangle is:

   1) 42 cm

   2) 52 cm

   3) 54 cm

   4) 56cm

   [tex] \huge { \blue{\fbox{ \red{ᴀnswer}}}}[/tex]

   ɢɪᴠᴇɴ:

   • ᴀʀᴇᴀ ᴏꜰ ᴛʀɪᴀɴɢʟᴇ = 1176 ᴄᴍᒾ
   • ʀᴀᴛɪᴏ ᴏꜰ ʙᴀꜱᴇ ᴛᴏ ᴀʟᴛɪᴛᴜᴅᴇ = 3:4

   ᴛᴏ ꜰɪɴᴅ:

   • ᴀʟᴛɪᴛᴜᴅᴇ

   ꜱᴏʟᴜᴛɪᴏɴ:

   ʟᴇᴛ ᴛʜᴇ ʙᴀꜱᴇ ʙᴇ ‘3x’ ᴀɴᴅ ᴀʟᴛɪᴛᴜᴅᴇ ʙᴇ ‘4x’

   [tex] \red\rightarrow1176 = \frac{1}{2} \times 3x \times 4x[/tex]

   [tex] \red \rightarrow1176 \times 2 = 3x \times 4x[/tex]

   [tex] \red \rightarrow2352 = 12 {x}^{2} [/tex]

   [tex] \red \rightarrow \frac{ \cancel{2352}}{ \cancel{12}} = {x}^{2} [/tex]

   [tex] \red \rightarrow196 = {x}^{2} [/tex]

   [tex] \red \rightarrow \sqrt{196} = \sqrt{ {x}^{2} } [/tex]

   [tex] \red \rightarrow14 = x[/tex]

   ᴀʟᴛɪᴛᴜᴅᴇ = 4x

   => 4x

   => 4 (14)

   =>56

   ᴏᴘᴛɪᴏɴ ɴᴏ.4 (56 ᴄᴍ) ɪꜱ ᴄᴏʀʀᴇᴄᴛ.

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