Question

Ththe area of four walls of a cuboid box is 256 CM square if the length of the box is 5 times the height and breadth is three times the height find the dimensions of the cuboidal box ​

Answer 1

$\huge\mathfrak\red{Answer ;}$

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$<b><I>Curved Surface area = 256cm^2$

So, let the Height be x

According to the Question,

Length is 5 times of height = 5x

Breadth is 3 times of height = 3x

Now,

2 [l+b]×h = 256

2 [5x + 3x] × x = 256

2 × 8x^2 = 256

16x^2 - 256 = 0

8 [2x^2 - 32] = 0 (Taking out 8 as common)

Now, through Factorization

2x^2 + 0x - 32 = 0

2x^2 + 8x^2 - 8x^2 - 32 = 0

[ 2x^2 + 8x^2 ] [ -8x^2 - 32 ] = 0

2x [x + 4] -8 [x + 4] = 0

[x + 4] [2x - 8] = 0

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• 2x - 8 = 0

2x = 8

x = 8/2 = 4

• x + 4 = 0

x = -4

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So,

X = 4

x = 4 (Sides Can't be Negative)

Henceforth,

Height = 4cm

Length = 5x = 5 × 4 = 20cm

Breadth = 3x = 3 × 4 = 12cm

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$\huge\mathfrak{Hope\: it\: Helps}$