Question

A square has a area of 144 a rectangle has the same perimeter as square if the breadth of the rectangle is 5 then find out the length of the rectangle ?​

Answer 1

Answer:

First find side of square

Let:length of side=x

Area of square =(side) ² ..........(formula)

144 =x²

12 =x .........(taking square root

on both sides)

therefore, x=12 unit

breath of rectangle =b=5unit

suppose :length of rectangle =ĺ

perimeter of squares= perimeter of rectangle

4(side) = 2(b+ĺ)

4× 12 =2(5+ĺ)

48 =10+2ĺ

2ĺ =38

ĺ =19 unit

Length of rectangle is 19 unit

Answer 2

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

$\mathfrak{ \: Suppose, \: } \\ \: \: \: \: \: \: \: \mathtt{The \: \: side \: \: of \: \: the \: \: square \: \: is = a} \\ \\ \underline{ \mathfrak{ \: \: Given, \: \: }} \: \: \\ \\ \: \: \: \: \: \: \: \boxed{ \bold{ \: \: </p><p>Area = 144 \: \: }}$

$\underline{ \mathfrak{ \: \: We \: \: know \: \: that, \: \: }} \\ \\ \boxed{ \bold{Area \: \: of \: \: a \: \: square = (Side) {}^{2} }} \\ \\ \underline{ \bold{A.T.Q.,}} \\ \\ \: \: \: \: \: \: \mathtt{(Side) {}^{2} = 144 } \\ \\ \mathtt{\Longrightarrow a {}^{2} = 144} \\ \\ \mathtt{\Longrightarrow a = 12} \\ \\ \mathtt{ \therefore \: \:Side \: \: of \: \: the \: square = 12 }$

$\mathtt{ \therefore \: \:Perimeter \: of \: \: the \: \: square = 4 \times side } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathtt{ = 4 \times 12}\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathtt{ = 48}$

$\mathfrak{Now,} \\ \: \: \: \: \: \: \: \underline{ \mathfrak{In \: \: case \: \: of \: \: the \: \: rectangle,}} \\ \\ \underline{ \mathfrak{ \: Given, \: }} \\ \: \: \: \: \: \: \: \: \: \: \: \mathtt{Breadth, b = 5} \\ \\ \underline{ \mathfrak{Suppose,}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathtt{Length = l} \\ \\ \mathtt{ \therefore \: \: </p><p>Perimeter \: \: of \: \: the \: \: rectangle = 2 (l + b) } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathtt{ = 2(l + 5)} \\ \\ \mathtt{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times l + 10} \\ \\ \bold{As \: \: perimeter \: \: of \: \: the \: \: rectangle \: \: is \: \: equal \: \: } \\ \bold{ to \: \: the \: \: perimeter \: \: of \: \: the \: \: square.} \\ \\ \: \: \: \: \: \: \: \: \: \mathtt{ 2 \times l + 10 = 48} \\ \\ \mathtt{\Longrightarrow 2 \times l = 48 - 10} \\ \\ \mathtt{\Longrightarrow 2 \times l = 38} \\ \\ \mathtt{\Longrightarrow l = \frac{38}{2} } \\ \\ \mathtt{ \therefore \: \: l = 19} \\ \\ \bold{ \therefore \: \: Length \: \: of \: \: the \: \: rectangle = 19}$