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
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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
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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
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
[tex]\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}[/tex]
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[tex]\dag\;{\underline{\frak{We\;know\;that,}}}[/tex]
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[tex]\star\;{\boxed{\pink{\sf{Area_{\;(Rectangle)} = l \times b}}}}[/tex]
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[tex]\dag\;{\underline{\frak{Putting\;values,}}}[/tex]
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[tex]:\implies\sf 7x \times 6x = 378[/tex]
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[tex]:\implies\sf 42x^2 = 378[/tex]
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[tex]:\implies\sf x^2 = \cancel{ \dfrac{378}{42}}[/tex]
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[tex]:\implies\sf x^2 = 9[/tex]
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[tex]:\implies\sf \sqrt{x^2} = \sqrt{9}[/tex]
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[tex]:\implies{\underline{\boxed{\sf{\pink{x = 3}}}}}\;\bigstar[/tex]
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★ Now, Put value of x in,
[tex]\therefore[/tex] Hence, Length and breadth of Rectangle is 21 cm and 18 cm respectively.
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[tex]\boxed{\underline{\underline{\bigstar \: \bf\:More\:to\:know\:\bigstar}}} \\ \\[/tex]