Answer: The dimensions are
Length = 11.25 inches
Width = 3.75 inches
Step-by-step explanation: The rectangle have been identified with clues as to the length and width (still unknown) and the measure of the perimeter has been given. We know that the perimeter is the measurement around the entire border of the shape and in a rectangle, the perimeter is given as
Perimeter = 2L + 2W or
Perimeter = 2(L + W)
However we are told that the length is three times the size of the width, which means whatever is the width, the length is going to be times 3. Simply put, if the width is expressed as W, then the length would be W x 3, which can also be expressed as 3W
So what we have now is
Length = 3W
Width = W
If the perimeter is 30 inches, then we can write out the expression
Perimeter = 2(L + W)
30 = 2(3W + W)
30 = 2(4W)
30 = 8W
Divide both sides of the equation by 8
W = 3.75.
With that in mind, we can now compute the size of the length which has been expressed as 3W.
If the length is 3W and the width is 3.75, then
Length = 3 x 3.75
Length = 11.25
