Question

The total surface area of a rectangular block is 846 cm2 . Find the length, breadth and height if these dimensions are in the ratio of 5:4:3.

Answer 1

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Let  the length be 5x

let the breadth be 4x

let the height be 3x

Surface Area of block=2(lb+bh+hl)

                           846=2(5x*4x+4x*3x+3x*5x)

                           423=(20x²+12x²+15x²)

                            423=47x²

                             9=x²

                             x=3

Length of the block=15cm

Breadth of the block=12cm

Height of the block=9cm

Answer 2

Given,

Ratio of LENGTH : BREADTH : HEIGHT =

5 : 4 : 3

Given,

$\rm T.S.A = 2 ( LB + BH + LH )$

LET x be taken common,

Therefore,

$\implies\rm 846 = 2 ( 5x \times 4x + 4x \times 3x + 3x \times 5x )$

$\implies\rm 846 = 2 \times 20 {x}^{2} + 12 {x}^{2} + 15 {x}^{2}$

$\implies\rm 846 = 2 \times 47 {x}^{2}$

$\implies\rm 846 = 94 {x}^{2}$

$\implies\rm 9 = {x}^{2}$

Therefore,

$\implies\rm x = 3$

Now substituting the value of x we get =

$\implies\rm LENGTH = 5 × 3 = 15 cm$

$\implies\rm BREADTH = 4 × 3 = 12 cm$

$\implies\rm HEIGHT = 3 × 3 = 9 cm$