Question

the breadth and the length not a rectangle are in the ratio of 6:7.if it's area is 378cm² ,find its breath and length​

Answer 1

Answer:

18=breadth nd 21=breadth

Step-by-step explanation:

let the breadth nd length be 6x nd 7x

area=l×b

378=(6x)(7x)

378=42x²

378/42=x²

9=x²

√9=x

3=x

breadth=6x=6×3=18

length=7x=7×3=21

Answer 2

Given Dimensions of a Rectangle are in ratio 6:7.

Area of Rectangle = 378 cm²

We have to find, measure Length and breadth.

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☯ Let length of Rectangle be 7x and breadth be 6x.

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⋆ Reference of image is shown in diagram

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\linethickness{0.4mm}\put(7.7,3){\large\sf{A}}\put(7.5,2){\sf{\large{6x}}}\put(7.7,1){\large\sf{B}}\put(9.3,0.7){\sf{\large{7x}}}\put(11.1,1){\large\sf{C}}\put(11.1,3){\large\sf{D}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\end{picture}$

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$\dag\;{\underline{\frak{We\;know\;that,}}}$

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$\star\;{\boxed{\pink{\sf{Area_{\;(Rectangle)} = l \times b}}}}$

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$\dag\;{\underline{\frak{Putting\;values,}}}$

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$:\implies\sf 7x \times 6x = 378$

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$:\implies\sf 42x^2 = 378$

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$:\implies\sf x^2 = \cancel{ \dfrac{378}{42}}$

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$:\implies\sf x^2 = 9$

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$:\implies\sf \sqrt{x^2} = \sqrt{9}$

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$:\implies{\underline{\boxed{\sf{\pink{x = 3}}}}}\;\bigstar$

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★ Now, Put value of x in,

• 6x = 6 × 3 = 18 cm
• 7x = 7 × 3 = 21 cm

$\therefore$ Hence, Length and breadth of Rectangle is 21 cm and 18 cm respectively.

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

• Perimeter of Rectangle = 2(l + b)

• Area of square = side × side

• Perimeter of Square = 4 × side

• Area of Circle = πr²

• Circumference of Circle = 2πr