Question

The Length breadth and height of a rectangular solid are in the ratio of 3 : 2 :1 and its total surface area is 352 CM square then find its length.

Answer 1

Given:-

• Ratio of Length, breadth and height is 3:2:1.
• Total surface area is 352cm^2.

To Find:-

• Find its length

Solution:-

Let consider length be 3x, breadth be 2x and height be x.

According to the question,

Using Formula:

$\: \: \sf \: total \: surface \: area = 2(lb + bh + lh)$

Now substitute the values,

$\: \: \sf \: total \: surface \: area = 2(3x \times 2x + 2x \times x + 3x \times x) \\ \\ \: \: \sf \:352 = 2(6 {x}^{2} + 2 {x}^{2} + 3 {x}^{2} ) \\ \\ \: \: \sf \: 352 = 2 \times 11 {x}^{2} \\ \\ \: \: \sf \: 352 = 22 {x}^{2} \\ \\ \: \: \sf \therefore \: x = \sqrt{ \frac{352}{22} } = \sqrt{16} = 4cm$

Hence,the value of x is 4 cm.

Therefore,

• Length = 3x = 3 × 4 = 12cm
• Breadth = 2x = 2 × 4= 8cm
• Height = x = 4cm

Answer 2

Answer:

☞︎︎︎Lᴇɴɢᴛʜ = 12 ᴄᴍ

Step-by-step explanation:

✫Gɪᴠᴇɴ :-

•Rᴀᴛɪᴏ ᴏғ Length breadth and height of a rectangular solid =3 : 2 :1

•Tᴏᴛᴀʟ sᴜʀғᴀᴄᴇ ᴀʀᴇᴀ = 352 ᴄᴍ ^2

✫ᴀssᴜᴍᴇ:-

• Lᴇɴɢᴛʜ = 3x

• Bʀᴇᴀᴅᴛʜ = 2x

• Hᴇɪɢʜᴛ = 1x ᴏʀ x

✫Fᴏʀᴍᴜʟᴀ:-

•Tᴏᴛᴀʟ sᴜʀғᴀᴄᴇ ᴀʀᴇᴀ ᴏғ ᴄᴜʙᴏɪᴅ = 2( ʟʙ + ʙʜ + ʜʟ)

✫Nᴏᴡ ғɪɴᴅ ᴀʀᴇᴀ:-

» 352= 2( 3x × 2x + 2x × x + x × 3x)

» 352= 2( 6x^2 + 2x^2 + 3x^2)

» 352= 2 × 11x^2

» 352= 22x^2

» x^2= 352/22

» x^2= 16

$\tt» \: \: x= \sqrt{16} = 4$

Sᴏ, ʟᴇɴɢᴛʜ = 3×4 = 12 ᴄᴍ

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