Question

Одна сторона прямокутника дорівнює 5 4/9 дм, а інша на 34/45дм більша від неї. Обчислити площу і периметер прямокутника. Швидко допоможіть!​

Answer 1

Problem Analysis

We are given the length of one side of a rectangle as 5 4/9 dm, and the other side is 34/45 dm larger than that. We need to calculate the area and perimeter of the rectangle.

Calculation

To find the area of a rectangle, we multiply the length and width. In this case, the length is given as 5 4/9 dm, and the width is 34/45 dm larger than that.

Let's calculate the width first: 5 4/9 dm + 34/45 dm = (5 * 9 + 4) / 9 dm + 34/45 dm = (45 + 4) / 9 dm + 34/45 dm = 49/9 dm + 34/45 dm

To add these fractions, we need to find a common denominator: 49/9 dm + 34/45 dm = (49/9 * 5/5) dm + 34/45 dm = 245/45 dm + 34/45 dm = (245 + 34) / 45 dm = 279/45 dm

Now that we have the width, we can calculate the area: Area = length * width = (5 4/9 dm) * (279/45 dm) = (49/9 dm) * (279/45 dm)

To multiply these fractions, we can multiply the numerators and denominators separately: Area = (49 * 279) / (9 * 45) dm^2

Now, let's calculate the perimeter of the rectangle. The perimeter is the sum of all four sides of the rectangle.

Perimeter = 2 * (length + width) = 2 * (5 4/9 dm + 279/45 dm)

To add these fractions, we need to find a common denominator: Perimeter = 2 * ((49/9 dm) + (279/45 dm)) = 2 * ((49 * 5/9 * 5) / (9 * 5) dm + (279/45 dm)) = 2 * ((245/9 dm) + (279/45 dm))

To add these fractions, we need to find a common denominator: Perimeter = 2 * ((245/9 * 5/5) / (9 * 5) dm + (279/45 dm)) = 2 * ((1225/45 dm) + (279/45 dm)) = 2 * ((1225 + 279) / 45 dm) = 2 * (1504/45 dm)

Now we can simplify the fractions: Area = (49 * 279) / (9 * 45) dm^2 = 13771/405 dm^2 Perimeter = 2 * (1504/45 dm) = 3008/45 dm

Answer

The area of the rectangle is 13771/405 dm^2 and the perimeter is 3008/45 dm.