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4 years ago

The perimeter of a rectangle is twice the sum

Mathematics

1 answer:

Rudiy274 years ago

8 0

The question is incomplete, here is the complete question:

The perimeter of a rectangle is twice the sum of its length and its width, the perimeter is 40 meters and the length is 2 meters more than twice its width. What is the length?

The length of the rectangle is 14 meters

Step-by-step explanation:

The formula of the perimeter of a rectangle is P = 2(L + W), where

L is its length
W is its width

Assume that the width of the rectangle is x meters

∵ The width of the rectangle = x meters

∵ Its length is 2 meters more than twice its width

- Multiply x by 2 and then add to the product 2

∴ The length of the rectangle = 2 x + 2 meters

∵ The formula of the perimeter is P = 2(L + W)

- Substitute L by 2 x + 2 and W by x

∴ P = 2(2 x + 2 + x)

- Add like terms in the bracket

∴ P = 2(3 x + 2)

- Simplify the right hand side

∴ P = 6 x + 4

∵ The perimeter of the rectangle = 40 meters

- Equate P by 40

∴ 6 x + 4 = 40

- Subtract 4 from both sides

∴ 6 x = 36

- Divide both sides by 6

∴ x = 6

∴ The width of the rectangle is 6 meters

∵ The length = 2 x + 2

- Substitute x by 6

∴ The length = 2(6) + 2 = 12 + 2 = 14 meters

The length of the rectangle is 14 meters

Learn more:

You can learn more about the rectangles in brainly.com/question/12919591

#LearnwithBrainly

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