Question

the perimeter of a rectangle is 150 cm. if the breadth of the rectangle is 25 CM. find its length. also find the area of the rectangle​

Answer 1

Given :

• Breadth of the Rectangle = 25 cm.

• Perimeter of the Rectangle = 150 cm.

To find :

• Length of the Rectangle.

• Area of the Rectangle.

Solution :

We know the formula for Perimeter of a Rectangle ,i.e,

$\boxed{\bf{P = 2(L + B)}}$

Where :

• P = Perimeter of the Rectangle.

• L = Length of the Rectangle.

• B = Breadth of the Rectangle.

$:\implies \bf{P = 2(L + B)}$

$:\implies \bf{150 = 2(L + 25)}$

$:\implies \bf{150 = 2L + 50}$

$:\implies \bf{150 - 50 = 2L}$

$:\implies \bf{100 = 2L}$

$:\implies \bf{\dfrac{100}{2} = L}$

$:\implies \bf{50 = L}$

$\boxed{\therefore \bf{L = 50\:cm}}$

Hence the length of the Rectangle is 50 cm.

Now , we know the formula for area of a Rectangle,i.e,

$\boxed{\bf{A = L \times B}}$

Where :

• P = Perimeter of the Rectangle.

• L = Length of the Rectangle.

• B = Breadth of the Rectangle.

$:\implies \bf{A = L \times B}$

$:\implies \bf{A = 50 \times 25}$

$:\implies \bf{A = 1250}$

$\boxed{\therefore \bf{A = 1250\:cm^{2}}}$

Hence the area of the Rectangle is 1250 cm².

Answer 2

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$\mathtt{\huge{\underline{\red{Answer\: :}}}}$

$\green{\frak{Given}} \begin{cases} \sf{Perimeter \: of \: a \: rectangle \: is \: 150 cm} \\ \sf{the \: breadth \: is \: 25cm } \\ \sf{length=?} \\ \sf{Area \: of \: the \: Rectangle =?} \end{cases}$

$\: \large \green{\bold{ \underline{ \: step \: by \: step \: explaination}}}$

$\: \\ \implies \displaystyle \bf \: perimeter \: of \: rectangle \: =2(l + b)$

$\: \implies \sf{ \: 150 = 2(25 + l)}$

$\: \implies \sf{150 = 50 + 2l}$

$\: \implies \sf \: 150 - 50 - 2l = 0$

$\: \implies \sf \: 100 = 2l$

$\: \implies \sf \: length = 50cm$

$\: \bullet \bf \underline{ \: area \: of \: rectangle = l \times b}$

$\: \\ \implies \sf \: area \: of \: rectangle = 50 \times 25$

$\: \implies \sf \: area \: of \: rectangle \: = 1250 \:$

$\: \: \boxed{ \underline{ \bold{area \: of \: the \: rectangle = 1250cm^2}}}$

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❄ Hope this answer helps u ⛄