Question

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​

Answer 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

$\sf \: 1176 = \dfrac{1}{2} \times 3x \times 4x$

$\sf \: 1176 \times 2 = 3x \times 4x$

$\sf \: 2352 = 12 {x}^{2}$

$\sf \dfrac{2352}{12} = {x}^{2}$

$\sf \:196 = {x}^{2}$

$\sf \: \sqrt{196} = \sqrt{ {x}^{2} }$

$\sf \: 14 = x$

Altitude = 4x

$\sf \: 4 x$

$\sf \: 4(14)$

$\sf \: 56$

Option 4

Answer 2

$\huge { \blue { \fbox{ \red{Qᴜᴇꜱᴛɪᴏɴ}}}}$

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

$\huge { \blue{\fbox{ \red{ᴀnswer}}}}$

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'

$\red\rightarrow1176 = \frac{1}{2} \times 3x \times 4x$

$\red \rightarrow1176 \times 2 = 3x \times 4x$

$\red \rightarrow2352 = 12 {x}^{2}$

$\red \rightarrow \frac{ \cancel{2352}}{ \cancel{12}} = {x}^{2}$

$\red \rightarrow196 = {x}^{2}$

$\red \rightarrow \sqrt{196} = \sqrt{ {x}^{2} }$

$\red \rightarrow14 = x$

ᴀʟᴛɪᴛᴜᴅᴇ = 4x

=> 4x

=> 4 (14)

=>56

ᴏᴘᴛɪᴏɴ ɴᴏ.4 (56 ᴄᴍ) ɪꜱ ᴄᴏʀʀᴇᴄᴛ.

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