Question

The dimension of a cuboid are in the ratio 3:4: 5 and its total surface area is 188 m2. Find the dimensions of cuboid ?

Answer 1

★ANSWER :

Dimensions of the cuboid are 3√2 m, 4√2 m and 5√2 m.

★EXPLANATION :

•Given :-

• Dimensions of the cuboid in the ratio = 3:4:5
• Total surface area = 188 m².

•To find :-

• Dimensions of the cuboid.

• Solution:-

Dimensions in ratio = 3:4:5

Consider,

Length of cuboid = 3x m.

Breadth of cuboid = 4x m.

Height of cuboid = 5x m.

We know,

${\boxed{\sf{Total\: surface\: area\:of\: cuboid=2(Length\times\: Breadth+Breadth\times\: Height+Length\times\: Height)}}}$

Total surface area ,

=2(3x × 4x + 4x × 5x + 3x × 5x) m²

=2(12x²+20x²+15x²) m²

=2 × 47x² m²

= 94x² m²

According to the question,

$\sf{94x^2=188}$

$\implies\sf{x^2=\frac{188}{94}}$

$\implies\sf{x=\sqrt{2}}$

So,

Length of the cuboid = 3√2 m

Breadth of the cuboid= 4√2 m

Height of the cuboid = 5√2 m

Hence dimensions of the cuboid are 3√2 m, 4√2 m and 5√2 m.

_______________________________

VERIFICATION :-

Length = 3√2 m

Breadth = 4√2 m

Height = 5√2 m

Total surface area of cuboid,

2(3√2×4√2+4√2×5√2+3√2×5√2) m²

=2(24 + 40 + 30) m²

= 188 m²

Total surface area of cuboid is 188 m².

_______________________________

Answer 2

$\huge \mathfrak{Answer:-}$

$\implies$length = 3x = 3√2

$\implies$breadth = 4x = 4√2

$\implies$height = 5x = 5√2

$\large\underline\mathrm{Given:-}$

• Diameter of the cuboid in the ratio 3:4:5
• Total surface area= 188m²

$\large\underline\mathrm{To \: find}$

• Dimention of the cuboid ratio 3:4:5.
• l = 3x
• b = 4x
• h = 5x

$\implies$ surface area of cuboid = 2(lb + bh + hl)

$\implies$2(3x × 4x + 4x × 5x + 5x × 3x)

$\implies$2(12x + 20x + 15x)m²

$\implies$94m²

$\implies$94x² = 188

$\implies$x² = 2

$\implies$x = √2

$\large\underline\mathrm{so, }$

$\implies$length = 3x = 3√2

$\implies$breadth = 4x = 4√2

$\implies$height = 5x = 5√2

$\large\underline\mathrm{hence,}$

$\large\underline\mathrm{dimensions \: of \: the \: cuboid \: are \: 3√2, \: 4√2, \: and \: 5√2m.</p><p>}$

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$