QuestionCalculate the area and perimeter of a rectangle with length $3\frac{16}{100}$ in and width $\frac{3}{8}$ in.

Studdy Solution

STEP 1

Assumptions1. The length of the rectangle is $3\frac{16}{100}$ inches. The width of the rectangle is $\frac{3}{8}$ inches3. The area of a rectangle is calculated by multiplying its length by its width4. The perimeter of a rectangle is calculated by adding twice the length and twice the width

STEP 2

First, we need to simplify the length of the rectangle. The length is given as a mixed number $\frac{16}{100}$ . We can simplify this by converting the fraction $\frac{16}{100}$ to its simplest form.

STEP 3

To simplify the fraction, we find the greatest common divisor (GCD) of the numerator and the denominator and then divide both by it.
The GCD of16 and100 is. So, we divide both the numerator and the denominator by.
$\frac{16}{100} = \frac{16 \div}{100 \div}$

STEP 4

Calculate the simplified fraction.
$\frac{16 \div4}{100 \div4} = \frac{4}{25}$

STEP 5

Replace the fraction in the mixed number with the simplified fraction to get the simplified length of the rectangle.
$Length =3\frac{4}{25}$

STEP 6

Now, we can calculate the area of the rectangle. The area of a rectangle is given by the formula $Area = Length \times Width$

STEP 7

Plug in the values for the length and the width to calculate the area.
$Area =3\frac{4}{25} \times \frac{3}{}$

STEP 8

Calculate the area of the rectangle.
$Area =3\frac{4}{25} \times \frac{3}{8} = \frac{100}{25}$

STEP 9

implify the fraction to get the area in simplest form.
$Area =4 \, square \, inches$

STEP 10

Now, we can calculate the perimeter of the rectangle. The perimeter of a rectangle is given by the formula $Perimeter =2 \times (Length + Width)$

STEP 11

Plug in the values for the length and the width to calculate the perimeter.
$Perimeter = \times (3\frac{4}{25} + \frac{3}{8})$

STEP 12

Calculate the perimeter of the rectangle.
$Perimeter =2 \times (\frac{4}{25} + \frac{}{8}) = \frac{200}{25}$

STEP 13

implify the fraction to get the perimeter in simplest form.
$Perimeter =8 \, inches$ The area of the rectangle is square inches and the perimeter is8 inches.

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