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Sagot :
Answer:
Length: 17 in, Width: 12 in
Step-by-step explanation:
Let l=length and w=width
l=w+5
2(w+5)+2w=58
4w=48
w=12, l=17
Answer:
- Length = 17 inches
- Width = 12 inches
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Step-by-step explanation:
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As it is given that, the length of a rectangle is 5 in longer than its width and the perimeter of the rectangle is 58 in and we are to find the length and width of the rectangle. So,
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Let us assume the width of the rectangle as x inches and therefore, the length will be (x + 5) inches .
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Now, According to the Question :
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[tex]{\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}[/tex]
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[tex]{\longrightarrow \qquad { {\sf{2 ( x + 5 + x )= 58 }}}}[/tex]
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[tex]{\longrightarrow \qquad { {\sf{2 ( 2x + 5 )= 58 }}}}[/tex]
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[tex]{\longrightarrow \qquad { {\sf{ 4x + 10= 58 }}}}[/tex]
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[tex]{\longrightarrow \qquad { {\sf{ 4x = 58 - 10}}}}[/tex]
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[tex]{\longrightarrow \qquad { {\sf{ 4x = 48}}}}[/tex]
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[tex]{\longrightarrow \qquad { {\sf{ x = \dfrac{48}{4} }}}}[/tex]
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[tex]{\longrightarrow \qquad{ \underline{ \boxed { \pmb{\mathfrak {x = 12}} }}} }\: \: \bigstar[/tex]
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Therefore,
- The width of the rectangle is 12 inches .
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Now, We are to find the length of the rectangle:
[tex]{\longrightarrow \qquad{ { \frak{\pmb{Length = x + 5 }}}}}[/tex]
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[tex]{\longrightarrow \qquad{ { \frak{\pmb{Length = 12 + 5 }}}}}[/tex]
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[tex]{\longrightarrow \qquad{ { \frak{\pmb{Length = 17}}}}}[/tex]
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Therefore,
- The length of the rectangle is 17 inches .
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