Question

find the side of a square whose area is equal tothe area of a rectangle whose dimenensions are 4 cm and 9 cm​

Answer 1

Answer:

6cm

Step-by-step explanation:

Given, length of a rectangle = 4 cm

Breadth of a rectangle = 9 cm

Area of a rectangle = length × breadth = 4 X9

= 36 cm²

As per question,

Area of square = Area of rectangle

Area of square = 36

s² = 36

s = √36

s = 6 cm

Answer 2

${ \large{ \underline{ \pmb{ \frak{Given : }}}}}$

★ The area of a square is equal to the area of a rectangle

★ The dimensions of the rectangle are 4cm and 9cm

${ \large{ \underline{ \pmb{ \frak{To \: Find : }}}}}$

★ The side of the square whose area is equal to that of a rectangle

${ \large{ \underline{ \pmb{ \frak{ Let's \: understand \: the \: concept : }}}}}$

☀️Concept : Here, we're provided with the dimensions of the rectangle and said that the area of the square is equal to the area of the rectangle. so, let's find the area of the rectangle so, that we may know the area of the square

❍ After we find the measure of the area of the square we can apply suitable formulae to find the side of the square.

${ \large{ \underline{ \pmb{ \frak{Using \: concept : }}}}}$

★ Formula to find the area of a rectangle according to the given measurements is length × breadth

★ Formula to find the area of a square is side times its side according to the what we have to find

${ \large{ \underline{ \pmb{ \frak{Solution }}}}}$

★ The side of the square is 6cm whose area is equal to that of a rectangle.

${ \large{ \underline{ \pmb{ \frak{ Full \: solution : \: }}}}}$

~ Firstly let's find the area of rectangle

❂ We know that the area of a rectangle = Length × breadth where length and breadth are 9cm and 4cm respectively.

➼ Area of the rectangle = Length × breadth

➼ Area of the rectangle = 9cm × 4cm

➼ Area of the rectangle = 36cm²

• Henceforth the area of the rectangle is 36cm²

~ As, we know that,

 ✦ The area of the rectangle is equal to that of the area of a square

• Henceforth, the area of the square is 36cm²

~ Now, let's find the side of the square

❂ We know that area of a square is equal to Side times its side

➼ Area of the square = Side × Side

➼ 36cm² = Side²

➼ Side = √ 36cm²

➼ Side = 6cm

• Henceforth the side of the square is 6cm

${ \large{ \underline{ \pmb{ \frak{Therefore : }}}}}$

★ The dimensions of the square are 6cm respectively.

${ \large{ \underline{ \pmb{ \frak{ Diagrams : }}}}}$

❍ Rectangle :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 9 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 4 cm}\end{picture}$

❍ Square :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){4}}\multiput(0,0)(0,4){2}{\line(1,0){4}}\put(-0.5,-0.5){\bf D}\put(-0.5,4.2){\bf A}\put(4.2,-0.5){\bf C}\put(4.2,4.2){\bf B}\put(1.5,-0.6){\bf\large 6\ cm}\put(4.4,2){\bf\large 6\ cm}\end{picture}$