Question

The floor of a rectangular banquet hall has an area of 3,600 m². The length is 90 m.

a. What is the width of the banquet hall?
b. A square banquet hall has the same area. What is the length of the room?
c. A third rectangular banquet hall has a perimeter of 3,600 m. What is the width if the length is 5 times the width?

Answer 1

Part a) The width of the rectangular banquet hall is 40 m

Part b) The length of the square room is 60 m

Part c) The width of the third rectangular banquet hall is 300 m

Explanation:

Part a) What is the width of the banquet hall?

Let

L ----> the length of the rectangular banquet hall

W ---> the width of the rectangular banquet hall

we know that

The area of a rectangle is equal to

`A=LW`

we have

`A=3,600\ cm^2`

`L=90\ m`

substitute the values and solve for W

`3,600=(90)W`

`W=3,600/(90)`

`W=40\ m`

therefore

The width of the rectangular banquet hall is 40 m

Part b) A square banquet hall has the same area. What is the length of the room?

we know that

The area of a square is

`A=L^2`

we have

`A=3,600\ cm^2`

substitute and solve for L

`3,600=L^2`

take the square root both sides

`L=60\ m`

therefore

The length of the square room is 60 m

Part c) A third rectangular banquet hall has a perimeter of 3,600 m. What is the width if the length is 5 times the width?

Let

L ----> the length of the third rectangular banquet hall

W ---> the width of the third rectangular banquet hall

we know that

The perimeter of a rectangle is equal to

`P=2(L+W)`

`3,600=2(L+W)`

simplify

`1,800=(L+W)` -----> equation A

`L=5W` ------> equation B

substitute equation B in equation A and solve for W

`1,800=(5W+W)`

`1,800=6W`

`W=300\ m`

therefore

The width of the third rectangular banquet hall is 300 m

Answer 2

we know,

in rectangle

area(a)=l*b

(a)so width (b)=a/l

=3600 m^2/90 m

=40m

(b) in square,

area(a)=l^2

or,3600 m^2=l^2

or,(60m)^2=l^2

cancelling square

length (l)=60m

(c) perimeter =2 (l+b)

let width be x so l is rd

or,3600m=2 (x+5x)

or,3600m/2=6x

or,1800m/6=x

or,300m=x (width) and length =5*x