Question

The perimeter of a rectangle is 75 cm .Its length is 11/4 times it's breath. Find the length and breadth. Find the length and breadth of the rectangle
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Answer 1

Answer:

L = 27.5 cm

B = 10 cm

Step-by-step explanation:

perimeter of rectangle = 2(L+B)

L = (11/4)*B (given)

75 = 2(11/4 + 1)B

75/2 = 15/4 B

10 cm = B

hence L = (11/4)*10

L = 2.75*10 = 27.5 cm

Answer 2

GivEn:

• Perimeter of a Rectangle = 75 cm

• Length of Rectangle is $\sf \dfrac{11}{4}$ times it's breadth.

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To find:

• Length and breadth of Rectangle.

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SoluTion:

★ Let's Breadth of Rectangle be b.

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Given that,

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Length of Rectangle is $\sf \dfrac{11}{4}$ times it's breadth.

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$:\implies\sf Length = \dfrac{11}{4}b$

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So, As we know that,

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$\star\;{\boxed{\sf{\purple{Perimeter\;of\; Rectangle = 2(l + b)}}}}$

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$\small\sf\;\;\;\; \underline{Put\;the\;given\;values\;:}$

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$:\implies\sf 75 = 2 \bigg( \dfrac{11}{4}b + b \bigg)$

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$:\implies\sf 75 = 2 \bigg( \dfrac{11b + 4b}{4} \bigg)$

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$:\implies\sf 75 = \cancel{2} \times \dfrac{15b}{ \cancel{4}}$

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$:\implies\sf 75 = \dfrac{15b}{2}$

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$:\implies\sf 75 \times 2 = 15b$

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$:\implies\sf 150 = 15b$

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$:\implies\sf b = \cancel{ \dfrac{150}{15}}$

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$:\implies{\underline{\boxed{\sf{\pink{Breadth\;(b) = 10\;cm}}}}}\;\bigstar$

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★ Now, Put the value of b in,

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$:\implies\sf Length = \dfrac{11}{4} \times 10$

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$:\implies\sf Length = \dfrac{110}{4}$

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$:\implies{\underline{\boxed{\sf{\blue{Length = 27.5\;cm}}}}}\;\bigstar$

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⋆ DIAGRAM:

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$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\linethickness{0.4mm}\put(7.7,3){\large\sf{A}}\put(7.5,2){\sf{\large{10 cm}}}\put(7.7,1){\large\sf{B}}\put(9.3,0.7){\sf{\large{27.5 cm}}}\put(11.1,1){\large\sf{C}}\put(11.1,3){\large\sf{D}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\end{picture}$

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$\therefore$ Hence, Dimensions of Rectangle (Length and breadth) are 27.5 cm and 10 cm respectively.