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

The perimeter of rectangle = 240 m

[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