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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 ...?

Respuesta :

syed514
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

Answer:

Option 3rd is correct

4: 3

Step-by-step explanation:

Perimeter(P) of rectangle is given by:

[tex]P =2(l+w)[/tex]

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.

[tex]\frac{\text{Perimeter of the larger rectangle}}{\text{Perimeter of the Smaller rectangle}}[/tex]

Substitute the given values we have;'

[tex]\frac{32}{24}=\frac{4}{3}[/tex]

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

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