Question

The length of a rectangle is 6 more than the width. The area is 720 square feet. Find the length and width of the rectangle.

Answer 1

Given :-

• The length of a rectangle is 6 more than the width

• Area of rectangle = 720 feet²

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To find:-

• Length
• Width

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Let :-

• Width of rectangle = x
• Length of rectangle = 6 + x

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Solution:-

So to find length and width of rectangle, we have to find value of x.

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We know:-

`\bigstar \boxed{ \rm Area~of~rectangle=Length*{}Width}`

By using this formula we can find value of x.

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So:-

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`\dashrightarrow\sf Area~of~rectangle=Length*{}Width \\`

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`\dashrightarrow\sf 720=(x + 6)(x)`

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`\dashrightarrow\sf 720=x(x) +x( 6)`

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`\dashrightarrow\sf 720= {x}^(2) +x( 6)`

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`\dashrightarrow\sf 720= {x}^(2) +6x`

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`\dashrightarrow\sf0 = {x}^(2) +6x - 720`

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`\dashrightarrow\sf {x}^(2) +6x - 720 = 0`

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`\dashrightarrow\sf {x}^(2) +30x - 24x - 720 = 0`

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`\dashrightarrow\sf ({x}^(2) +30x )- 24x - 720 = 0`

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`\dashrightarrow\sf x({x}+30 )- 24x - 720 = 0`

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`\dashrightarrow\sf x({x}+30 ) + (- 24x - 720) = 0 \\`

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`\dashrightarrow\sf x({x}+30 ) - 24(x+ 30) = 0 \\`

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`\dashrightarrow\sf (x - 24)({x}+30 )= 0 \\`

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We got two solutions:-

first solution

• x - 24 = 0
• x = 24

Second solution :-

• x + 30 = 0
• x = -30

Length can't be taken negative so 24 is the value of x.

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Value of width:-

• Width of rectangle = x
• Width = 24 feet

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Value of Length:-

• Length of rectangle = x + 6
• Length = 24 + 6
• Length = 30 feet