Question

The ratio of the length and breadth of a rectangle is
3:1. If the perimeter is 64 cm, find the dimensions of
the rectangle. (Only iintelligents will ans)​

Answer 1

Answer:

2(3x+x) = 64

2 × 4x = 64

8x = 64

x = 64 ÷ 8

x = 8 cm

Length = 24cm

Breadth = 8 cm

Hope this helps...

Answer 2

Answer :-

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Question\;:-}}}$

Here the concept of Perimeter of Rectangle has been used. We see we are given the ratio of Length and Breadth of the Rectangle. So their must be a constant x by which the ratio should be multiplied to get the original value. Then we can apply that in the formula of Perimeter of Rectangle.

Let's do it !!

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★ Formula Used :-

$\\\;\boxed{\sf{Perimeter\;of\;Rectangle\;=\;\bf{2\;\times\;(Length\;+\;Breadth)}}}$

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★ Solution :-

Given,

» Ratio of length and breadth = 3 : 1

» Perimeter of Rectangle = 64 cm

• Let the constant be 'x'.

Then,

» Length of Rectangle = 3x

» Breadth of Rectangle = 1x

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~ For the value of x ::

$\\\;\;\;\sf{:\Longrightarrow\;\;\;Perimeter\;of\;Rectangle\;=\;\bf{2\;\times\;(Length\;+\;Breadth)}}$

$\\\;\;\;\sf{:\Longrightarrow\;\;\;64\;=\;\bf{2\;\times\;(3x\;+\;1x)}}$

$\\\;\;\;\sf{:\Longrightarrow\;\;\;64\;=\;\bf{2\;\times\;(4x)}}$

$\\\;\;\;\sf{:\Longrightarrow\;\;\;64\;=\;\bf{8x}}$

$\\\;\;\;\sf{:\Longrightarrow\;\;\;x\;=\;\bf{\dfrac{64}{8}}}$

$\\\;\;\;\sf{:\Longrightarrow\;\;\;x\;=\;\bf{8}}$

Hence, x = 8

Now by applying the value of x in the Length and Breadth, we get,

» Length = 3x = 3(8) = 24 cm

$\\\;\underline{\boxed{\tt{Length\;\;of\;\;Rectangle\;\;=\;\bf{24\;\;cm}}}}$

» Breadth = x = 8 cm

$\\\;\underline{\boxed{\tt{Breadth\;\;of\;\;Rectangle\;\;=\;\bf{8\;\;cm}}}}$

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★ More to know :-

$\\\;\sf{\leadsto\;\;Area\;of\;Rectangle\;=\;Length\;\times\;Breadth}$

$\\\;\sf{\leadsto\;\;Area\;of\;Square\;=\;(Side)^{2}}$

$\\\;\sf{\leadsto\;\;Area\;of\;Circle\;=\;\pi r^{2}}$

$\\\;\sf{\leadsto\;\;Area\;of\;Triangle\;=\;\dfrac{1}{2}\;\times\;Base\;\times\;Height}$

$\\\;\sf{\leadsto\;\;Area\;of\;Parallelogram\;=\;Base\;\times\;Height}$