The area of a rectangle is 247 cm^2. The width and length are both whole numbers greater than 1. What are the dimensions of the rectangle?
What two prime numbers would multiply to give you 247? To help, what two numbers would multiply to give 7 in the ones space?
21 and 3
To find the dimensions of a rectangle given its area, you need to consider the factors or pairs of numbers whose product equals the given area. In this case, the area is 247 cm^2.
Start by listing the factors of 247: 1, 13, 19, and 247. Now, check if any pair of these factors meets the conditions of being whole numbers greater than 1.
Let's examine each pair:
1 * 247 = 247
Although this pair gives the desired product, it does not meet the condition that the dimensions are greater than 1.
13 * 19 = 247
This pair also gives the desired product, and both 13 and 19 are greater than 1. Therefore, the dimensions of the rectangle are 13 cm and 19 cm.
Hence, the rectangle has dimensions 13 cm by 19 cm.