Respuesta :
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:
- 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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[tex]{\longrightarrow \qquad{ {{\boldsymbol {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}}[/tex]
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[tex]{\longrightarrow \qquad {\rm{2(w + 2 + {w})= 32 \ }}}[/tex]
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[tex]{\longrightarrow \qquad {\rm 2({2w + 2= 32 ) }}}[/tex]
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[tex]{\longrightarrow \qquad {\rm{4w +4= 32 \ }}}[/tex]
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[tex]{\longrightarrow \qquad {\rm{4w = 28\ }}}[/tex]
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[tex]{\longrightarrow \qquad {\rm{w = \dfrac{28}{4} }}}[/tex]
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[tex]{\longrightarrow \qquad{ \mathfrak{{\pmb{w = 7 }}}}}[/tex]
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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:
[tex]{\longrightarrow \qquad{ {{\rm{Length = w + 2 }}}}}[/tex]
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[tex]{\longrightarrow \qquad{ {{ \rm{Length = 7 + 2 }}}}}[/tex]
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[tex]{\longrightarrow \qquad{ { \frak{ \pmb{Length = 9}}}}}[/tex]
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Now, we are to find the area of the rectangle :
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[tex]{\longrightarrow \qquad{ {{\boldsymbol{ Area_{(Rectangle)} = Length \times Breadth }}}}}[/tex]
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[tex]{\longrightarrow \qquad{ {{ \rm{ Area_{(Rectangle)} = 9 \times 7 }}}}}[/tex]
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[tex]{\longrightarrow \qquad{ { \pmb{\boldsymbol{ Area_{(Rectangle)} = 63 }}}}}[/tex]
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Therefore,
- The area of the rectangle is 63 ft².
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