Question

external dimensions of a closed wooden box are in the ratio 5:4:3.if the cost of painting its outer surface at the rate of rs5 per dm^2s rs 11750 find dimensions of the box

Answer 1

Answer:

Length=125dm, Breadth=100dm, Height=75dm

Step-by-step explanation:

Given external dimensions of a closed wooden box are in the ratio 5:4:3.if the cost of painting its outer surface at the rate of Rs 5 per $dm^2$ Rs 11750. we have to find the dimension of box.

Let length=5x, breadth=4x and height=3x

T.S.A=$2(LB+BH+HL)$

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

        =$2(20x^2+12x^2+15x^2)=94x^2$

Also given outer surface at the rate of Rs 5 per $dm^2$ Rs 11750.

∴ $T.S.A=5(11750)=58750dm^2$

Hence, equating we get

$94x^2=58750$

⇒ $x^2=625$ ⇒ x=25

Hence, Length=5x=5(25)=125dm

            Breadth=4x=4(25)=100dm

            Height=3x=3(25)=75dm

       

Answer 2

Answer:

Length=125dm, Breadth=100dm, Height=75dm

Step-by-step explanation:

Given external dimensions of a closed wooden box are in the ratio 5:4:3.if the cost of painting its outer surface at the rate of Rs 5 per dm^2dm2 Rs 11750. we have to find the dimension of box.

Let length=5x, breadth=4x and height=3x

T.S.A=2(LB+BH+HL)2(LB+BH+HL)

        =2(5x\times 4x+4x\times 3x+3x\times 5x)2(5x×4x+4x×3x+3x×5x)

        =2(20x^2+12x^2+15x^2)=94x^22(20x2+12x2+15x2)=94x2

Also given outer surface at the rate of Rs 5 per dm^2dm2 Rs 11750.

∴ T.S.A=5(11750)=58750dm^2T.S.A=5(11750)=58750dm2

Hence, equating we get

94x^2=5875094x2=58750

⇒ x^2=625x2=625 ⇒ x=25

Hence, Length=5x=5(25)=125dm

            Breadth=4x=4(25)=100dm

            Height=3x=3(25)=75dm