Question

The dimensions of a smaller rectangle are 3 ft. by 9 ft. The dimensions of a larger rectangle are 5 ft. by 11 ft. Find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle. Options are 11:9, 3:4, 4:3, and 5:3 ...?

Answer 1

Option 3rd is correct

4: 3

Explanation:

Perimeter(P) of rectangle is given by:

`P =2(l+w)`

where, l is the length and w is the width of the rectangle respectively.

Given that:

The dimensions of a smaller rectangle are 3 ft. by 9 ft.

Perimeter of smaller rectangle= 2(3+9) =2(12) = 24 ft.

It is also given that: The dimensions of a larger rectangle are 5 ft. by 11 ft.

Perimeter of Larger rectangle = 2(5+11) =2(16) = 32 ft.

We have to find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle.

`\frac{\text{Perimeter of the larger rectangle}}{\text{Perimeter of the Smaller rectangle}}`

Substitute the given values we have;'

`(32)/(24)=(4)/(3)`

Therefore, the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle is, 4 : 3

Answer 2

perimeter of smaller rect = 2L + 2B = 2*3ft + 2*9ft = 2(3 + 9) ft perimeter of bigger rect = 2L + 2B = 2*5ft + 2*11ft = 2(5 + 11) ft perimeter of larger rect 2(3 + 9) ft 12 3 --------------------- = ----------- = ------ = ----- perimeter of smaller rect 2(5 + 11) ft 16 4 so their ratio is 3:4