Question

The floor of a rectangular hall has a perimeter 300 cm.Let the cost of painting of four walls at a rate of Rs.12 per square cm is Rs.24000, then find the height of the wall

Answer 1

Let the length, breadth, and height of the rectangular floor be l, b and h cm respectively.

We know that,

Perimeter of the floor of the hall=2(l+b)

Given perimeter= 300cm

Therefore,

2(l+b)=300

(l+b)= 300/2

=150 cm......(i)

Now we know that,

Area of 4 walls= Area of cuboid - Area of floor - Area of top

Here,

Area of cuboid = 2(lb+bh+lh)

Area of floor = lxb

Area of top= lxb

Therefore,

Area of 4 walls= 2(lb+bh+lh)-lb-lb

=2(lb) +2(bh)+2(lh)-2(lb)

=2(lh)+2(bh)

=2h(l+b)

=2h x 150 [from (i)]

=300h

So,

Area of 4 walls = 300h Square cm

Cost of painting per square cm area= Rs 12

Therefore,

Cost of painting per square cm area

= Rs (12 x 300h)

= Rs 3600h

According to the question,

24000=3600h

Therefore,

h= 24000/3600

=6.66 cm