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Nat2105 [25]
2 years ago
12

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.

Mathematics
2 answers:
Hoochie [10]2 years ago
6 0
<h3>Given :-</h3>
  • The length of a rectangle is 6 more than the width

  • Area of rectangle = 720 feet²

\\

<h3>To find:-</h3>
  • Length
  • Width

\\

<h3>Let :-</h3>
  • Width of rectangle = x
  • Length of rectangle = 6 + x

\\

<h3>Solution:-</h3>

So to find length and width of rectangle, we have to<u> find value of x.</u>

\\

We know:-

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

By using this formula we can find value of x.

\\

So:-

\\

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

\\

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

\\

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

\\

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

\\

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

\\

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

\\

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

\\

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

\\

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

\\

\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 \\

\\

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

\\

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.

\\

Value of width:-

  • Width of rectangle = x
  • Width = 24 feet

\\

Value of Length:-

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

Vesna [10]2 years ago
5 0

Answer:

the length is 30 square feet the width is 24 square feet

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