Question

The floor of a rectangle has a perimeter of ®250 m . if the cost of painting the four walls at the rate of ®10 per m² is 15000 find the height of the wall

Answer 1

⇒ Formulas which will be used here ;

1. LSA of Cubiod = 2(l+b)h

2. Floor of rectangle (Perimeter) = 2(l+b)

⇒ Solving as per question ;

1. LSA = Area of all 4 walls.

→  2(l+b)h $\bold{m^2}$         .....(i)

2. Floor's Perimeter = 2(l+b)

= 250m = 2(l+b)

= $\bold{\frac{250}{2}}$ = (l+b)

 = $\bold{\frac{\cancel{250}^{\:\:125}}{\cancel{2}_{\:\:1}}}$ = (l+b)

∴ (l+b) = 125 m.

Putting this value in (i),

2(l+b)h = 2(125)h .

Now, According to the question ;

1$\bold{m^2}$ = ₹10

∴₹15000 =$\frac{Rs.\:15000}{Rs.\:10}$

=$\frac{Rs.\:1500\cancel{0}}{1\cancel{0}}$

= 1500$\bold{m^2}$

∴ LSA = 1500$\bold{m^2}$

∴ 2(l+b)h = 1500$\bold{m^2}$

∴ 2(125)h = 1500$\bold{m^2}$

∴ $\bold{h\:=\:\frac{1500}{250}{m^2}}$

∴ $\bold{h\:=\:\frac{150\cancel{0}}{25\cancel{0}}{m^2}}$

∴ $\bold{h\:=\:\frac{\cancel{150}^{\:\:30}}{\cancel{25}_{\:\:5}}{m^2}}$

∴ $\bold{h\:=\:\frac{\cancel{30}^{\:\:6}}{\cancel{5}_{\:\:1}}{m^2}}$

∴ h = 6m

∴ Height of wall = 6m

Thanks!