Question

The floor of a rectangular banquet hall has an area of 3,600 square meters. The length is 90m. 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 has a perimeter of 3,600 m. What is the width if the length is 5 times the width?

Answer 1

(a) Width of the banquet hall `"40 meters"`

(b) Length of the room `"60 meters"`

(c) Width of the rectangular banquet hall `"300 meters"`

Explanation:

The floor of a rectangular banquet hall has an area of 3,600 square meters.

The length is 90m.

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

Area of rectangle = Length * Width

So, Length * Width = 3,600 Sq.meters.

`rArr 90*Width = 3600`

Divide both sides 90.

`rArr (90*Width)/90=3600/90`

`rArr (cancel 90*Width)/cancel 90=3600/90`

`rArr Width = "40 meters"`

b.) A square banquet hall has the same area,

What is the length of the room?

Area of Square [A] ** = `s ^2`, `color(red)s` being the Side of the square.

In a square, all the sides are congruent.

`A=3600`

Hence, Side * Side = 3600

`Side^2 = 3600`

`Side =sqrt(3600)`

`Side = "60 meters"`

c.) A third rectangular banquet has a perimeter of 3,600 m.

What is the width if the length is 5 times the width?

Let Width = x meters.

Hence, Length = 5 * Width = 5*x = 5x.

Given that the Perimeter of the rectangle = 3600 meters.

Perimeter of the rectangle = 2 * [ Length + Width ]

So,

2 * [ Length + Width ] = 3600

`rArr 2*[5x+x]=3600`

`rArr 2*(6x)=3600`

`rArr 12x=3600`

`x=3600/12`

`x=300`

Hence Length = 5 * x = 5 * 300 = 1500 meters.

Width = 300 meters.

Hope it helps.