The perimeter of a rectangular
backyard is 6x + 6 yards. If the width is x yards, find a binomial that represents the length.
The perimeter minus twice the width is twice the length. Therefore
Length = (1/2)(6x + 6 -2x) = 2x + 3
To find the binomial that represents the length of the rectangular backyard, we need to understand what the perimeter represents. The perimeter of a rectangle is the sum of all its sides.
In this case, the perimeter is given as 6x + 6 yards. We know that a rectangle has two pairs of equal sides. So, the sum of the lengths of the two pairs of equal sides should be equal to the given perimeter.
Let's break down the given perimeter: 6x + 6.
We can divide this into two parts: 6x and 6.
The width of the rectangle is given as x yards. So, one pair of equal sides is x yards long.
To find the length, we need to subtract the width from the perimeter. Therefore, the length can be represented as:
(6x + 6) - x
Simplifying this expression, we get:
5x + 6
Hence, the binomial that represents the length of the rectangular backyard is 5x + 6.