Question

The perimeter of a rectangle is 62 m. The length is four more than two times the width. What is the length?

Answer 1

We can translate these sentences into equations:

"The perimeter of a rectangle is 62 m"

`\sf P=2l+2w`

`\sf 62=2l+2w`

"The length is four more than two times the width."

`\sf l=2w+4`

Now we can plug in what 'l' equals in the 2nd equation into the first equation:


`\sf 62=2l+2w`


`\sf 62=2(2w+4)+2w`

Distribute:


`\sf 62=4w+8+2w`

Combine like terms:


`\sf 62=6w+8`

Subtract 8 to both sides:


`\sf 54=6w`

Divide 6 to both sides:


`\sf w=9`

So this is our width, we can plug this into any of the two equations to find the length:


`\sf l=2w+4`


`\sf l=2(9)+4`

Multiply:


`\sf l=18+4`

Add:


`\boxed{\sf l=22~m}`

Answer 2

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Define length and width
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Let x be the width
width = x
Length = 2x + 4

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Formula
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Perimeter = 2(length + width)

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Find Length and width
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62 = 2(2x + 4 + x)
62 = 2(3x + 4) ← combine like terms
62 = 6x + 8 ← remove bracket
62 - 8 = 6x ← minus 8 on both sides
6x = 54 ← swap sides
x = 54 ÷ 6 ← divide by 6 on both sides
x = 9 m

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Find Length and Width
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Width = x = 9 m
Length = 2x + 4 = 2(9) + 4 = 22 m

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Answer: Length = 22m
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