Mathematics, 25.12.2019 12:31 leianagaming

The length and breadthof a rectangular playground are in the ratio 7: 5.the perimeter of the playground is 288m. what is its area?

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Answer from: StupidFatChipmunk

5040m²

Step-by-step explanation:

To find the area of a rectangle, use the area formula. A = lw

"l" is for length and "w" is for width or breadth.

To find "A", area, we need the length and width.

Use the information about perimeter to find the length and width.

The perimeter of a rectangle is calculated with the formula P = 2(l + w)

"P" for perimeter.

Just like the area formula, "l" for length and "w" for width/breadth.

Given the playground's ratio, it's like there is a small version of the real playground.

The real playground like is a scaled up version of the ratio. The two rectangles are related by a scale factor (how much bigger/smaller the rectangles are to each other).

The ratio rectangle has the length 7 and width 5.

First, find the perimeter of the ratio rectangle using the formula.

P = 2(l + w) Substitute 7 for length, "l", and 5 for width, "w"

P = 2(7 + 5) Solve inside the brackets first

P = 2(12) Simplify by multiplying

P = 24 Perimeter of ratio rectangle

Compare the perimeters of the ratio rectangle and the real playground.

To find the scale factor, divide the real perimeter by the ratio perimeter.

288 ÷ 24 = 12 The playground is 12 times larger than the ratio rectangle.

Using the scale factor and the ratio rectangle's dimensions, we can find the length and width of the real playground. Multiply each of the ratio rectangle's dimensions by 12, the scale factor.

Length of playground = 7 X 12 = 84

Width or breadth of playground = 5 X 12 = 60

To make sure the playground is 84m by 60m, check using the perimeter formula.

P = 2(l + w) Substitute "l" for 84 and "w" for 60

P = 2(84+60) Add inside the brackets

P = 2(144) Multiply

P = 288 Same perimeter as in question. 84 and 60 are correct.

Substitute the real playground's length and width into the area formula.

A = lw

A = (84m)(60m) Multiply numbers and units. (metres X metres is m²)

A = 5040m² Area of playground

Therefore, the area of the playground is 5040m².