Question

The length of a rectangle is 3 inches greater than its width. The perimeter is less than 54

Answer 1

The dimensions of rectangle can anyone from the set $\{1 \times 4,2 \times 5,3 \times 6,4 \times 7,5 \times 8,6 \times 9,7 \times 10,8 \times 11,9 \times 12,10 \times 13,11 \times 14\}$

Solution:

Given that , The length of a rectangle is 3 inches greater than its width.

The perimeter is less than 54 inches.  

Now, let the width of the rectangle be "n" inches. Then, the length of the rectangle will be n + 3 inches.

perimeter = 2(length + width)

Substituting the values, we get,

perimeter = 2(n + 3 + n)  = 2 (2n + 3)  

perimeter = 4n + 6  

Now, we are given that, perimeter is less than 54

Then, perimeter < 54

4n + 6 < 54

4n < 54 – 6  

4n < 48  

n < 12  

So, that, the width of the rectangle can be any value less than 12 inches.

Such  that the values of width of rectangle are from 1 to 11

And corresponding length of rectangle are 1 + 3 to 11 +3 ⇒ 4 to 14

Thus Dimensions of rectangle can anyone from the set $\{1 \times 4,2 \times 5,3 \times 6,4 \times 7,5 \times 8,6 \times 9,7 \times 10,8 \times 11,9 \times 12,10 \times 13,11 \times 14\}$