Question

a rectangle has an area equal to that of a square of side 35 cm. if the breadth of the rectangle is 25 cm, find its length.​

Answer 1

Answer:

Dɪᴀɢʀᴀᴍs :

☼ Figure of square :-

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){4}}\multiput(0,0)(0,4){2}{\line(1,0){4}}\put(-0.5,-0.5){\bf D}\put(-0.5,4.2){\bf A}\put(4.2,-0.5){\bf C}\put(4.2,4.2){\bf B}\put(1.5,-0.6){\bf\large{35\ cm}}\put(4.4,2){\bf\large{35\ cm}}\end{picture}$

━┅━┅━┅━┅━┅━┅━┅━┅━┅━┅━

☼ Figure of rectangle :-

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large{Lenght}}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large{25\ cm}}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

$\begin{gathered}\end{gathered}$

Gɪᴠᴇɴ :

• A rectangle has an area equal to that of a square of side 35 cm.
• The breadth of the rectangle is 25 cm.

$\begin{gathered}\end{gathered}$

Tᴏ Fɪɴᴅ :

• Lenght of rectangle

$\begin{gathered}\end{gathered}$

Usɪɴɢ Fᴏʀᴍᴜʟᴀs :

$\longrightarrow\small{\underline{\boxed{\pmb{\sf{Area \: of \: square = {(a)}^{2}}}}}}$

$\longrightarrow\small{\underline{\boxed{\pmb{\sf{Area \: of \: rectangle = {(l \times b)}}}}}}$

Where :-

• a = side
• l = length
• b = breadth

$\begin{gathered}\end{gathered}$

Sᴏʟᴜᴛɪᴏɴ :

Finding the area of square by substituting the values in the formula :-

$\dashrightarrow\small{\sf{Area \: of \: square = {(a)}^{2}}}$

$\dashrightarrow\small{\sf{Area \: of \: square = {(side)}^{2}}}$

$\dashrightarrow\small{\sf{Area \: of \: square = {(25)}^{2}}}$

$\dashrightarrow\small{\sf{Area \: of \: square = {(25 \times 25)}}}$

$\dashrightarrow\small{\underline{\boxed{\sf{\red{Area \: of \: square = {625 \: {cm}^{2}}}}}}}$

∴ Area of square is 625 cm².

━┅━┅━┅━┅━┅━┅━┅━┅━┅━┅━

☼ Now, According to the question :-

$\dashrightarrow{\small{\sf{Area \: of \: square = Area \: of \: rectangle}}}$

$\dashrightarrow{\small{\sf{{(Side)}^{2} = Lenght \times Breadth}}}$

$\dashrightarrow{\small{\sf{1225= Lenght \times 25}}}$

$\dashrightarrow{\small{\sf{ Lenght = \dfrac{1225}{25}}}}$

$\dashrightarrow{\small{\sf{ Lenght = \cancel{\dfrac{1225}{25}}}}}$

$\dashrightarrow{\small{\sf{ Lenght = 49 \: cm }}}$

$\dashrightarrow{\small{\underline{\boxed{\sf{\red{ Lenght = 49\: cm }}}}}}$

∴ The lenght of rectangle is 49 cm.

$\begin{gathered}\end{gathered}$

Vᴇʀɪғɪᴄᴀᴛɪᴏɴ :

$\dashrightarrow{\small{\sf{Area \: of \: square = Area \: of \: rectangle}}}$

$\dashrightarrow{\small{\sf{{(Side)}^{2} = Lenght \times Breadth}}}$

$\dashrightarrow{\small{\sf{{(35)}^{2} = 49 \times 25}}}$

$\dashrightarrow{\small{\sf{{(35 \times 35)}= 1225}}}$

$\dashrightarrow{\small{\sf{1225 \: {cm}^{2} = 1225 \: {cm}^{2} }}}$

$\dashrightarrow{\small{\underline{\boxed{\sf{\red{LHS = RHS}}}}}}$

∴ Hence Verified!

$\begin{gathered}\end{gathered}$

Lᴇᴀʀɴ Mᴏʀᴇ :

$\begin{gathered}\begin{gathered}\boxed{\begin {minipage}{9cm}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}p\sqrt {4a^2-p^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {minipage}}\end{gathered}\end{gathered}$

$\underline{\rule{200pt}{2.5pt}}$

Answer 2

☼Given:

• Area of Rectangle=Area of Square
• Breadth of Rectangle=25 Cm
• Side of Square=35 Cm

☼To find:

✯Length of Rectangle✯

☼Formulae:

• Length of Rectangle=Area/Breadth
• Area of Square=Side×Side

☼Solution:

Firstly let's find the area of Square

➠Side×Side

➛35×35

➛1225 Cm²

As given in the Question Area of Square=Area of Rectangle

➬1225Cm²=1225Cm²

Now, Let's Calculate Length of Rectangle

➠Length=Area/Breadth

➛Length=1225/25

➛Length=49Cm

∴Hence 49Cm is the Correct Answer!