Question

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. Write the equation that represents the situation. What is the width of the postage stamp? What is the length of the postage stamp?

Answer 1

Answer:

- The equation is: $\frac{249}{2}=2(x+\frac{17}{4})+2x$

- The width of the postage stamp is 29 milimeters.

- The length is 33.25 milimeters.

Step-by-step explanation:

1. The length ($y$) is $4^{\frac{1}{4} }mm=\frac{17}{4}mm$ longer than the width ($x$):

$y=x+\frac{17}{4}$

2. The perimeter is $124^{\frac{1}{2}}mm=\frac{249}{2}mm$.

3. The perimeter of a rectangle is:

$Perimeter=2Length+2Width$

4. Substitute values:

$\frac{249}{2}=2(x+\frac{17}{4})+2x$

5. Solve for the width $x$:

$\frac{249}{2}=2x+\frac{34}{4}+2x\\x=\frac{116}{4}\\x=29$

6. Calculate the length:

$y=x+\frac{17}{4}\\y=29+\frac{17}{4}\\y=33.25$