Question

length of a rectangle exceeds its bredth by 4m if the perri
meter of the rectangle is 84 m find its length and breadth

Answer 1

Answer:

• Length = 23 m
• Breadth = 19 m

Step-by-step explanation:

As per the provided information in the given question, we have :

• Length of a rectangle exceeds its bredth by 4 m or it is 4 m more than the breadth.
• The perimeter of the rectangle is 84 m.

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We are asked to find the measure of its length and breadth.

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Let us assume the breadth as 'b'.As per the given question length is 4 m more than its breadth. So,

$\longrightarrow \sf { Length = 4 \: m + Breadth }$

$\longrightarrow \sf { Length = 4 \: m + b }$

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Let it be the equation (1).

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Now, as we know that,

$\underline{ \boxed{ \sf{Perimeter_{(Rectangle)} =2 \Big(Length + Breadth \Big) }}}$

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$\longrightarrow \sf { 84 = 2( \ell + b )}$

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Substitute the value of length from the equation (1) to find the value of breadth.

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$\longrightarrow \sf { 84 = 2( 4 +b+ b )}$

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$\longrightarrow \sf { 84 = 2( 4 +2b )}$

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$\longrightarrow \sf { \dfrac{84}{2} = ( 4 +2b )}$

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$\longrightarrow \sf { 42 = 4 + 2b}$

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$\longrightarrow \sf { 42 -4= 2b}$

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$\longrightarrow \sf { 38 = 2b}$

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$\longrightarrow \sf {b = \dfrac{38}{2}}$

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$\longrightarrow \boxed{ \sf { 19 \: m = Breadth }}$

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Now, substitute the value of breadth in the equation (1) to find the measure of length of rectangle.

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$\longrightarrow \sf { Length = 4 \: m + Breadth }$

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$\longrightarrow \sf { Length = 4 \: m + 19 \: m }$

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$\longrightarrow \boxed{\sf { Length = 23 \: m }}$

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Therefore, length and breadth of the rectangle is 23 m and 19 m respectively.