Question

HELP ⚠️50 points⚠️

Please state your explanation, I got 6 (just checking my answer)

Two different rectangles have the same width. All four sides and both rectangles have integer lengths. The areas of the rectangles are 1086 and 828. Find the largest possible value of the common width of rectangles.

Answer 1

2 different rectangles have the same width. All four sides of both rectangles

have integer lengths. The areas of the rectangles are 1086 and 828. Find the largest possible value of the common width of the rectangles?

:

Since all dimensions are integers, it makes sense to prime factor the areas:

:

1086 = 2 * 3 * 181

:

828 = 2 * 2 * 3 * 3 * 23

:

The highest common factor is 3

:

The width is 3,

:

Large rectangle length: 1086/3 = 362

:

Small rectangle length: 828/3 = 276