Question

The sides of a rectangle are in the ratio 5 : 4 and its perimeter is 90 cm. What will be its length and breadth?

Answer 1

Given:

• Ratio of the sides of a rectangle is 5:4.
• Perimeter of rectangle = 90 cm

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To find:

• Length and breadth of rectangle?

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☯ Let length and breadth of rectangle be 5x and 4x respectively.

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$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 5x cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 4x cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

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$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Perimeter_{\;(rectangle)} = 2(length + breadth)}}}}$

Here,

• Length = 5x
• Breadth = 4x
• Perimeter = 90 cm

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$:\implies\sf 2(5x + 4x) = 90$

$:\implies\sf 2 \times 9x = 90$

$:\implies\sf 18x = 90$

$:\implies\sf x = \cancel{ \dfrac{90}{18}}$

$:\implies{\underline{\boxed{\frak{\purple{x = 5}}}}}\;\bigstar$

Therefore,

• Length of rectangle, 5x = 5 × 5 = 25 cm
• Breadth of rectangle, 4x = 4 × 5 = 20 cm

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$\qquad\qquad\boxed{\underline{\underline{\pink{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}}$

• Area of rectangle = length × breadth

• Diagonal of rectangle = √(length)² + (breadth)

• Area of square = side × side

• Perimeter of square = 4 × side

• Diagonal of square = √2 × side

Answer 2

Answer:

Step-by-step explanation:

let the side be 5x and 4x

perimeter = 2( length + breadth)

90 = 2(5x+4x)

90 = 18x

x = 90/18

x = 5

length = 5x

           = 5×5 = 25 cm

Breadth = 4x

             = 4×5 = 20 cm