Question

The perimeter of rectangle is equal to the perimeter of square with side 14cm. If the breadth of rectangle is 9cm. Find its length

Answer 1

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

FORMULA USED

$\boxed{ \bold {\red{ \rightsquigarrow : Perimeter \: \: of \: \: a \: \: square = 4 \times side}}} \\ \\ \boxed{ \bold{ \red{ \rightsquigarrow: Perimeter \: \: of \: \: a \: \: rectangle = 2 (length + breadth)}}}$

$\underline{ \mathfrak{ \: We \: \: have \: \: to \: \: find : \mapsto}} \\ \\ \text{Length of the rectangle = ? } \\ \\ \underline{\mathfrak{ \: Given, \: }} \\ \\ \: \: \mathtt{The \: \: side \: \: of \: \: the \: \: square, a = 14 cm} \\ \\ \mathtt{\therefore \: Perimeter \: \: of \: \: the \: \: square = 4a } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathtt{= (4 \times 14) cm } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathtt{= 56 \: cm}</p><p>$

$\mathfrak{Also,} \\ \: \: \: \: \: \: \underline{ \mathfrak{Given \: \: that,}} \\ \\ \: \: \: \: \: \: \: \: \text{Perimeter of the rectangle is equal to the} \\ \text{ perimeter of the square.} \\ \\ \mathfrak{And,} \\ \\ \text{Breadth of the rectangle, b = 9 cm} \\ \\ \underline{ \mathfrak{Suppose,}} \\ \\ \: \: \: \: \: \: \: \text{Length of the rectangle = l}$

$\underline{ \bold{ \: \: A.T.Q., \: \: }} \\ \\ \: \: \: \: \: \: \: \: \mathtt{2 (l + b) = 4a} \\ \\ \mathtt{ \Longrightarrow \: 2(l + 9) = 56 } \\ \\ \mathtt{ \Longrightarrow \:2 \: l + 18 = 56 } \\ \\ \mathtt{ \Longrightarrow \: 2 \: l = 56 - 18} \\ \\ \mathtt{ \Longrightarrow \: 2 \: l = 38} \\ \\ \mathtt{ \Longrightarrow \:l = \frac{38}{2} } \\ \\ \: \: \: \mathtt{ \therefore \: \underline{ \: l = 19 \: }} \\ \\ \\ \mathtt{ \underline{ \: : \rightsquigarrow : } \: \: Length \: \: of \: \: the \: \: rectangle = 19 \: cm}$