Question

6. The perimeter of rectangle is 20cm. If the length of rectangle is 6cm, then its breadth will be:

a) 4 cm

b) 6 cm

c) 10 cm

d) 14 cm​

Answer 1

Answer:

breadth will be 4 cm

is this correct

much time after I solve math questions

Answer 2

$\large\sf\underline{Given\::}$

• Perimeter of the rectangle = 20 cm

• Length of the rectangle = 6 cm

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$\large\sf\underline{To\:find\::}$

• Breadth of the rectangle

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$\large\sf\underline{Concept\::}$

Here we are given the Perimeter of rectangle as 20 cm and the length as 6 cm . We are asked to calculate the breadth of the rectangle . For that we would equate the given value of perimeter with the formula for Perimeter of the rectangle . Doing so we would get our required result . So let's begin !

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$\large\sf\underline{Formula\:to~be~used\::}$

• Perimeter of the rectangle = $\large{\mathfrak{2(l+b)}}$

where , l stands for length and b for breadth.

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$\large\sf\underline{Solution\::}$

We know :

$\sf\:Perimeter~of~the~rectangle~=~2(l+b)$

• Substituting the given value of perimeter

$\sf\implies~20=~2(l+b)$

• Substituting the given value of length

$\sf\implies~20=~2(6+b)$

• Multiplying the terms in RHS

$\sf\implies~20=~12+2b$

$\sf\implies~oR~12+2b~=~20$

• Transposing +12 to other side it becomes -12

$\sf\implies~2b~=~20-12$

$\sf\implies~2b~=~8$

• Now transposing 2 to other side it goes to the denominator

$\sf\implies~b~=~\frac{8}{2}$

• Reducing the fraction to the lower terms

$\sf\implies~b~=~\cancel{\frac{8}{2}}$

$\small{\underline{\boxed{\mathrm\red{{\mathfrak{\implies\:b~=~4~cm}}}}}}$ ★

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$\large\sf\underline{Verifying\::}$

We got our answer as option (a) = 4cm .

So let's check if it's correct . For checking we would substitute the value of a and b we got in the formula of perimeter an equate it with the given value of perimeter. Doing so if we get LHS = RHS our answer would be correct.

$\sf\:Perimeter~of~the~rectangle~=~2(l+b)$

$\sf\implies~20=~2(6+4)$

$\sf\implies~20=~2(10)$

$\sf\implies~20=~2 \times 10$

$\sf\implies~20=~20$

$\bf\implies~LHS~=~RHS$

$\bf\color{marron}{Hence~Verified}$

‎_______________________________

$\dag\:\underline{\sf So\:the\:required\:breadth\:is\:4~cm\:that\:is\:option\:(a).}$‎

!! Hope it helps !!