Question

The area of a floor is 864 sq. m. and its perimeter is 120m.

Answer 1

Answer:

Area of rectangular carpet = 120 sq meters. Also area of a rectangle is product of its length(l) and breadth(b). So, area = l * b = 120

So l = 120 / b (by cross multiplying) …..(i)

Perimeter of rectangle is = 46 meter. Also the perimeter of a rectangle can be written as Perimeter= 2 * (l + b)

So 46 = 2 * (l + b) …..(ii)

Substituting (i) in (ii) we get,

46 = 2 * ( 120/b + b)

which can also be written as,

b^2 - 23b + 120 = 0

By middle spilting we get

b^2 - 15b - 8b + 120 = 0

so b = 15 or 8.

Assume b=8 then from (i) l = 120/8 => l=15

Now in a right angled triangle

H^2 = L^2 + B^2

H^2 = (15)^2 + (8)^2

H^2 = 225 + 64 = 289

therefore H = 17

So the length of the diagonal is 17 meters.

The area of given rectangle is =120 m^2

Area of rectangle is= length×breadth

Let's say length = l

Breadth =b

Now , perimeter of rectangle is =2(l+b)

Perimeter is=46m

Now, 2 ( l+b)=46

Square on both sides

4(l+b)^2=2116

(l+b)^2=529

Open the whole square

l^2+b^2+2 (l×b)=529

Put the value of l×b= 120

l^2+b^2=529–240

l^2+b^2=289

We know that diagonal is √l^2+b^2

So answer is √289

17 m

hope it helps you