Question

The length of a rectangle is 2ft longer than it’s width. If the perimeter of the rectangle is 32 ft, find it’s area

Answer 1

Answer:

• Area of rectangle is 63 feet²

Step-by-step explanation:

Given:

• The length of a rectangle is 2ft longer than it’s width.
• If the perimeter of the rectangle is 32 ft

To Find:

• Area of the rectangle.

Solution:

Let's assume Width of rectangle be x feet and length be 2 +x. to Find the are of the rectangle firstly we need to the length and width of the Rectangle:

Using formula:

• Perimeter of rectangle = 2(L + B)

→ 32 = 2(x + 2 + x)

→ 32 = 2(2x + 2)

→ 32 = 4x + 4

→ 32 - 4 = 4x

→ 28 = 4x

→ 28/4 = x

→ 7 = x

Hence,

• Length of the rectangle = 2 + x = 9 feet
• Width of the rectangle = x = 7 feet.

Now,

→ Area of rectangle = Length × Width

→ Area fo rectangle = 9 × 7

→ Area of rectangle = 63 feet²

• Hence, Area of the rectangle is 63 feet²

Answer 2

Answer:

• 63 sq.ft

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Step-by-step explanation:

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• As it is given that, the length of a rectangle is 2ft longer than it’s width and perimeter of the rectangle is 32 ft.

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So, let us assume the width of the rectangle as w ft and therefore the length will (w + 2) ft .

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Now,

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${\longrightarrow \qquad{ {{\boldsymbol {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}}$

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${\longrightarrow \qquad {\rm{2(w + 2 + {w})= 32 \ }}}$

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${\longrightarrow \qquad {\rm 2({2w + 2= 32 ) }}}$

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${\longrightarrow \qquad {\rm{4w +4= 32 \ }}}$

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${\longrightarrow \qquad {\rm{4w = 28\ }}}$

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${\longrightarrow \qquad {\rm{w = \dfrac{28}{4} }}}$

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${\longrightarrow \qquad{ \mathfrak{{\pmb{w = 7 }}}}}$

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• Therefore width of the rectangle is 7 ft .

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Now, We are to find the length of the rectangle:

${\longrightarrow \qquad{ {{\rm{Length = w + 2 }}}}}$

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${\longrightarrow \qquad{ {{ \rm{Length = 7 + 2 }}}}}$

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${\longrightarrow \qquad{ { \frak{ \pmb{Length = 9}}}}}$

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Now, we are to find the area of the rectangle :

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${\longrightarrow \qquad{ {{\boldsymbol{ Area_{(Rectangle)} = Length \times Breadth }}}}}$

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${\longrightarrow \qquad{ {{ \rm{ Area_{(Rectangle)} = 9 \times 7 }}}}}$

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${\longrightarrow \qquad{ { \pmb{\boldsymbol{ Area_{(Rectangle)} = 63 }}}}}$

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Therefore,

• The area of the rectangle is 63 ft².

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