Question:-
the ratio between the length and the breadth of a rectangle is 4:5 and the perimeter is 240 meters. the dimensions of the rectangle.
Solutions:-
Given that,
The ratio between the length and the breadth of a rectangle is 4 : 5.
Let assume that
Length of rectangle, l = 4x meter
Breadth of rectangle, b = 5x meter
Further, given that
[tex]\begin{gathered}\rm \: Perimeter_{(Rectangle)} = 240 \\ \end{gathered}[/tex]
[tex]\begin{gathered}\rm \: 2(4x + 5x) = 240 \\ \end{gathered}[/tex]
[tex]\begin{gathered}\rm \: 9x = 120 \\ \end{gathered}[/tex]
[tex]\begin{gathered}\bf\implies \:x = \dfrac{40}{3} \: m \\ \end{gathered}[/tex]
So,
[tex]\begin{gathered}\bf\implies \:Length = 4x = \dfrac{160}{3} \: m \\ \end{gathered}[/tex]
[tex]\begin{gathered}\bf\implies \:Breadth = 5x = \dfrac{200}{3} \: m \\ \end{gathered}[/tex]
[tex]\rule{190pt}{2pt}[/tex]
[tex]\large{Question:-}[/tex]
Given:
The area of rectangle = 3375 m2
• The perimeter of a ractangle = 240 m
• The ratio of its length and breadth is 5: 3 .
Formulae:
• The perimeter of rectangle = 2( l + b )
• The area of rectangle = l × b
where,
• l = length of rectangle
• b = Breadth of rectangle
Solution:
According to this question
The ratio its length and breadth = 5:3
let the length = 5x
and breadth = 3x
[tex]\begin{gathered}2(5x + 3x) = 240 \\ \: \implies8x = \frac{\cancel2\cancel4\cancel0}{\cancel2} \\ \implies \: x = \frac{\cancel1\cancel2\cancel0}{\cancel8}15 \\ \: \implies \: x = 15\end{gathered}[/tex]
The length of rectangle = 5x = 5×15 = 75 m
breadth of rectangle = 3x = 3×15 = 45 m
• The area of rectangle =
[tex]75 \times 45 = 3375 \: {m}^{2}[/tex]
So the area of rectangle = 3375 m2
[tex]\blue{\texttt{Answer}}[/tex]
• The area of rectangle = 3375 m2
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Answers & Comments
Question:-
the ratio between the length and the breadth of a rectangle is 4:5 and the perimeter is 240 meters. the dimensions of the rectangle.
Solutions:-
Given that,
The ratio between the length and the breadth of a rectangle is 4 : 5.
Let assume that
Length of rectangle, l = 4x meter
Breadth of rectangle, b = 5x meter
Further, given that
[tex]\begin{gathered}\rm \: Perimeter_{(Rectangle)} = 240 \\ \end{gathered}[/tex]
[tex]\begin{gathered}\rm \: 2(4x + 5x) = 240 \\ \end{gathered}[/tex]
[tex]\begin{gathered}\rm \: 9x = 120 \\ \end{gathered}[/tex]
[tex]\begin{gathered}\bf\implies \:x = \dfrac{40}{3} \: m \\ \end{gathered}[/tex]
So,
[tex]\begin{gathered}\bf\implies \:Length = 4x = \dfrac{160}{3} \: m \\ \end{gathered}[/tex]
[tex]\begin{gathered}\bf\implies \:Breadth = 5x = \dfrac{200}{3} \: m \\ \end{gathered}[/tex]
[tex]\rule{190pt}{2pt}[/tex]
Verified answer
[tex]\large{Question:-}[/tex]
the ratio between the length and the breadth of a rectangle is 4:5 and the perimeter is 240 meters. the dimensions of the rectangle.
Given:
The area of rectangle = 3375 m2
• The perimeter of a ractangle = 240 m
• The ratio of its length and breadth is 5: 3 .
Formulae:
• The perimeter of rectangle = 2( l + b )
• The area of rectangle = l × b
where,
• l = length of rectangle
• b = Breadth of rectangle
Solution:
According to this question
The ratio its length and breadth = 5:3
let the length = 5x
and breadth = 3x
[tex]\begin{gathered}2(5x + 3x) = 240 \\ \: \implies8x = \frac{\cancel2\cancel4\cancel0}{\cancel2} \\ \implies \: x = \frac{\cancel1\cancel2\cancel0}{\cancel8}15 \\ \: \implies \: x = 15\end{gathered}[/tex]
So,
The length of rectangle = 5x = 5×15 = 75 m
breadth of rectangle = 3x = 3×15 = 45 m
• The area of rectangle =
[tex]75 \times 45 = 3375 \: {m}^{2}[/tex]
So the area of rectangle = 3375 m2
[tex]\blue{\texttt{Answer}}[/tex]
• The area of rectangle = 3375 m2