Question

the ratio between length breadth and height of the rectangular block 3: 2:1 and its total surface area is 352 CM² find the length of block​

Answer 1

Solution

Given :-

• the ratio between length breadth and height of the rectangular block 3: 2:1
• total surface area is 352 cm² .

Find :-

• Length of rectangular block .

Explanation

Using Formula

$\boxed{\tt{\red{\:(Surface\:area_{Rectangular\:block}\:=\:2(LB+BH+HL)}}}$

Where,

• L = length .
• B = Breadth
• H = Height

Now, let .

• Length be = 3x
• Breadth be = 2x
• Height be = x

keep value,

==> Total surface area of rectangular block = 2(3x.2x + 2x.x + x.3x)

==> 352 = 2(6x² + 2x² + 3x²)

==> (11x²) = 352/2

==> 11x² = 176

==> x² = 176/11

==> x² = 16

==> x² = 4²

==> x = 4 .

Hence

• Length be of Rectangular block = 3x = 3×3 = 12 cm
• Breadth be of rectangular block = 2x = 2×4 = 8 cm
• Height be of Rectangular block = x = 4 cm.

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Answer 2

Answer:

☞︎︎︎Lᴇɴɢᴛʜ ᴏғ ʙʟᴏᴄᴋ = 12 ᴄᴍ

Step-by-step explanation:

✫Gɪᴠᴇɴ:-

•the ratio between length breadth and height of the rectangular block =3: 2:1

•Tᴏᴛᴀʟ sᴜʀғᴀᴄᴇ ᴀʀᴇᴀ = 352 ᴄᴍ²

✫Tᴏ ғɪɴᴅ :-

•Lᴇɴɢᴛʜ ᴏғ ᴛʜᴇ ʙʟᴏᴄᴋ

✫Assᴜᴍᴇ:-

•Lᴇɴɢᴛʜ ʙᴇ 3x

•ʙʀᴇᴀᴅᴛʜ ʙᴇ 2x

•ʜᴇɪɢʜᴛ ʙᴇ 1x ᴏʀ x

✫Fᴏʀᴍᴜʟᴀ:-

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

✪Nᴏᴡ ғɪɴᴅ ʙʏ ᴋᴇᴇᴘ ᴛʜᴇɪʀ ᴠᴀʟᴜᴇs ɪɴ ғᴏʀᴍᴜʟᴀ,

$\tt \to352 = 2( 3x × 2x + 2x × x + x × 3x) \\ \tt \to \frac{352}{2} = 6 {x}^{2} + 2 {x}^{2} + 3 {x}^{2} \\ \tt \to176 = 11 {x}^{2} \\ \tt \to \frac{176}{11} = {x}^{2} \\ \tt \to16 = {x}^{2} \\ \tt \to x = \sqrt{16} = 4$

✫Hᴇɴᴄᴇ :-

•Lᴇɴɢᴛʜ = 3x = 3×4 = 12 ᴄᴍ

•Bʀᴇᴀᴅᴛʜ = 2x = 2×4 = 8ᴄᴍ

•Hᴇɪɢʜᴛ = 1x = 1×4 = 4ᴄᴍ

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