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The yard behind cindy's house is rectangular in shape and has a perimeter of 72 feet. If the length is l of the yard 18 feet longer than the width of the yard, what is the area of the yard in square feet

Verified Answer :

Using concepts for the perimeter and area of rectangle, it is found that:

The area of the yard is of 243 square feet.

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Rectangle:

A rectangle of length l and width w has:

  • Perimeter given by \(P = 2(l + w)\)
  • Area given by \(A = lw\)

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  • Perimeter of 72 feet means that \(P = 72\)
  • Length 18 longer than the width means that: \(l = 18 + w\)

Relating the measures, we find them, first the width:

\(2(l + w) = 72\)

\(l + w = 36\)

\(18 + w + w = 36\)

\(2w = 18\)

\(w = \frac{18}{2}\)

\(w = 9\)

Then the length:

\(l = 18 + w = 18 + 9 = 27\)

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The area is:

\(A = lw = 27 \times 9 = 243\)

The area of the yard is of 243 square feet.

A similar problem is given at https://brainly.com/question/10489198

The area of the yard is : A = 243 ft²

The dimensions of the yard are:

l = 27 ft

w = 9 ft

Perimeter "p" is:

p = 2×l + 2×w

Where w is the width

According to the problem statement

p = 72 ft .  and

l = w + 18 .    ⇒        w . = l - 18

Then

72  = 2×l + 2× ( l - 18 )

Solving the equation we get:

72 = 2×l + 2×l - 2× 18

72 = 4×l - 36

72 + 36 = 4×l

l = 27 ft

and .   w = 27  - 18 .         w = 9 ft

Then the area of the yard  A is:

A = l×w .       A = 27×9

A = 243 ft²