Question

The area of a rectangle is the product of its length and width. Both length and width are whole numbers. A rectangular poster has an area of 204 square inches. The width of the poster is greater than 10 inches and is prime. What is the width of the poster?

Answer 1

Answer:

17 inches.

Step-by-step explanation:

If the area of a rectangle is the product of its length and width, then;

Area of a rectangle = Length × Width

Given that the width of the poster is greater than 10 inches and is prime, this means and W>10

Area of the rectangle = 204in²

On substituting the values in the formula;

A = LW

204 = LW

Since W is greater than 10 and is prime, it can be between the prime numbers 11, 13 and 17. Note that L must be a whole number as well for any number to be the right answer we seek.

Let's test each values of the prime width that will give a length that is a whole number.

If W = 11

204 = 11×L

L = 204/11

L = 18.54

Since the length didn't give us a whole number, this means our width is not 11.

If W = 13

204 = L × 13

L = 204/13

L = 15.69

Also, we can see that the length is not also a whole number for the value of 13 as the prime width.

If W = 17

204 = L × 17

L = 204/17

L = 12

It can be seen that the length of the rectangle gave us a whole number when we used the prime width of 17, hence the width of the poster that is greater than 10 inches and is prime that makes both length and width to be a whole number is 17 inches.