Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
Answer:
- 14 m
Step-by-step explanation:
Let the shorter side be x
Then the longer side is x + 1
Perimeter is:
- P = 2( x + x + 1) = 2(2x + 1) = 4x + 2
The value of perimeter is at most 60 meters. P ≤ 60.
Solve the inequality:
- 4x + 2 ≤ 60
- 4x ≤ 58
- x ≤ 58/4
- x ≤ 14.5
Since x is the integer, its greatest value is 14 m
[tex]{ \large{ \red{➾ \: \: \underline {\bf{ \underline{Let \: \: the \: \: width \: \: of \: \: rectangle \: \: be \: \: y}}}}}}[/tex]
[tex]{ \large{ \blue{➾ \: \: \underline {\bf{ \underline{Then \: \: the \: \: length \: \: of \: \: rectangle \: \: be \: \: (y + 1)}}}}}}[/tex]
[tex]{ \large{ \green{✪ \: \: \boxed{ \boxed{ \rm{Perimeter \: \: of \: \: rectangle = 2 \times (length + breadth)}}}}}}[/tex]
[tex]{ \large{ \pink{⇛ \: \: \sf{Perimeter = 2 \times (y + y + 1)}}}}[/tex]
[tex]{ \large{ \orange{⇛ \: \: \sf{Perimeter = 4y + 2}}}}[/tex]
[tex]{ \large{ \purple{ ✒ \: \: \: \tt{Here \: \: given = \: Perimeter \: \: is \: \: at \: \: most \: \: 60 \: m}}}}[/tex]
[tex]{ \large{ \red{ ⇝ \: \bf{So \: \: perimeter \leqslant 60}}}}[/tex]
[tex]{ \large{ \green{ \underline{ \rm{Now \: \: we \: \: have \: \: to \: \: solve \: \: inequality}} \colon}}}[/tex]
[tex]{ \large{ \blue{➠ \: \: \bf{4y + 2 \leqslant 60}}}}[/tex]
[tex]{ \large{ \orange{➠ \: \: \bf{4y \leqslant 58}}}}[/tex]
[tex]{ \large{ \purple{➠ \: \: \bf{y \leqslant { \cancel\dfrac{58} {4 }^ { \: \: {14.5}} {}} }}}}[/tex]
[tex]{ { \blue{➠ \: \: \bf{y(Width \: \: of \: \: rectangle ) \: \: \leqslant 14.5 \: \: \: { \underline{ \underline{(But \: \: y \: \: is \: \: an \: \: integer)}}}}}}} [/tex]
[tex]{ \large{ \rm{ \green{ ∴ \: \: \: \: { \boxed{ \boxed{\bf{y \: (Width \: \: of \: \: rectangle ) \: \: greatest \: \: value \: = 14 \: \: m \: \: \:{ \underline{ \underline{}}}}}}} }}} \: \: { \large{ \green{ \rm{Ans.}}}}}[/tex]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.