Question

solve quickly plz..........

Answer 1

Hope u like my process
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Lateral Surface Area :-
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The total surface area of the body excluding the top and bottom face .

For a cuboid
============
Lateral Surface Area = Perimeter of the base × Height = 2(l+b)×h

where

l= length

b = breadth

h = height

________________________

Given
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=> L.S.A = 486m²

=> Breadth = 12 m

=> Ratio of length and height = 5:3

=> Length = 5x m (Let)

=> height = 3x m

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By problem
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=> 2(5x + 12)×3x = 486

=> x(5x + 12) = 486÷6 = 81

=> 5x² + 12x -81 = 0

=> 5x² + 27x - 15x -81 =0

=> x(5x +27) -3(5x + 27)=0

=>(x -3)(5x +27) =0

since length cant be negative

so. x -3 = 0

=> x = 3

_____________________

=> Required length = l = 5×3 = 15 m

=> Required height = h = 3×3 = 9 m
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Hope this is your required answer

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Answer 2

$\small \text{ANSWER}$



LATERAL SURFACE AREA :


For a cubiod :

L.S.A = Perimeter of the base × height

» 2 (l + b) × h

_______________________


GIVEN :

» Lateral surface area = 486 m²

» Ratio of length and height = 5:3

» Breadth = 12 m

» Height = 3x m

» Length = 5x m


_______________________


Now,

› 2 (5x + 12) × 3x = 486

› x (5x + 12) = 486 ÷ 6 = 81

› 5x² + 12x - 81 = 0

› 5x² + 27x - 15x - 81 = 0

› x (5x + 27) - 3 (5x + 27) = 0

› (x + 3) (5x + 27) = 0

_______________________

Length can't be negative


Therefore, x - 3 = 0
x = 3

_______________________

LENGTH :

» 5 × 3 = 15 m


HEIGHT :

» 3 × 3 = 9 m


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