The length of a postage stamp is 4 1/4 millimeters longer than its width. The perimeter of the stamp is 124 1/2 millimeters. What is the width of the postage stamp? What is the length of the postage stamp?

Question

Eva Abramson · Accepted Answer

The length and width of the postage stamp are #33 1/4 mm and 29 mm# respectively.

Let the width of the postage stamp be #x# mm Then, the lengtth of the postage stamp be #(x+4 1/4)#mm. Given perimeter is #P=124 1/2 # We know perimeter of a rectangle is #P=2(w+l)#; where #w# is the width and #l# is the length. So #2(x+x+ 4 1/4) = 124 1/2 or 4x+ 8 1/2 = 124 1/2 or 4x =124 1/2- 8 1/2 or 4x =116 or x = 29 :. x+4 1/4=33 1/4# The length and width of the postage stamp are #33 1/4 mm and 29 mm# respectively.[Ans]

Eva Adamson · Answer

undefined Let's denote the width of the postage stamp as "w" millimeters.

Given that the length of the postage stamp is 4 1/4 millimeters longer than its width, we can express the length as "w + 4 1/4" millimeters.

The formula for the perimeter of a rectangle (which the stamp resembles) is P = 2(length + width).

Substituting the given values, we have:
124 1/2 = 2(w + w + 4 1/4)

Simplify and solve for "w":
124 1/2 = 2(2w + 4 1/4)
124 1/2 = 4w + 8 1/2
116 = 4w
w = 29

So, the width of the postage stamp is 29 millimeters.

Now, we can find the length using the expression we derived earlier:
Length = w + 4 1/4
Length = 29 + 4 1/4
Length = 33 1/4

So, the length of the postage stamp is 33 1/4 millimeters.