# If the area of a triangle is 1176 cm² and base : corresponding altitude is 3:4, then the altitudeof the triangle is: December 16, 2021 by Charlie

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​

## Given :–

Area of triangle = 1176 cm²

Ratio of base to altitude = 3:4

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

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

• 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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