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

2 thoughts on “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”

1. 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

   [tex] \tt» \: \: x= \sqrt{16} = 4[/tex]

   Sᴏ, ʟᴇɴɢᴛʜ = 3×4 = 12 ᴄᴍ

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2. 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:

   [tex] \: \: \sf \: total \: surface \: area = 2(lb + bh + lh)[/tex]

   Now substitute the values,

   [tex] \: \: \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[/tex]

   Hence,the value of x is 4 cm.

   Therefore,

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

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