Question

The sides of a rectangular piece of paper are in the ratio 2:3. Of the area is 150 square cm , find the length of its side ​

Answer 1

Given: The sides and of a rectangular piece of paper are in the ratio 2:3.

Need to find: The length of its side.

❒ Let the sides Length and Breadth of a rectangular piece be 2x and 3x respectively.

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀

$\underline{\boldsymbol{According\: to \:the\: Question :}}$

⠀⠀⠀

• The area of rectangular piece is 150 cm².

⠀⠀

$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\; that\; :}}$

⠀

$\star\:\boxed{\sf{\pink{Area_{\:(rectangle)} = Length \times Breadth}}}$

⠀

Therefore,

⠀

$:\implies\sf 2x \times 3x = 150 \\\\\\:\implies\sf 6x^2 = 150 \\\\\\:\implies\sf x^2 = \cancel\dfrac{150}{6}\\\\\\:\implies\sf x^2 = 25 \\\\\\:\implies\sf x = \sqrt{25} \\\\\\:\implies{\underline{\boxed{\frak{\purple{x = 5}}}}}\:\bigstar$

⠀

Hence,

⠀

• Length, 2x = 2(5) = 10 cm
• Breadth, 3x = 3(5) = 15 cm

⠀

$\therefore\:{\underline{\sf{Hence, \ the\; required\; \ Length \: \ is\: \bf{10\; cm}.}}}$

Answer 2

Step-by-step explanation:

$\frak {Given} \begin{cases} &\sf{Ratio\ of\ given\ sides\ =\ \bf 2\ :\ 3.} \\ &\sf{Area\ =\ \bf 150cm^2.} \end{cases}$

To find:- We have to find the length of its side ?

☯️ Let the length and breadth of the rectangular piece of paper be 2x and 3x.

__________________

$\frak{\underline{\underline{\dag As\ we\ know\ that:-}}}$

$\sf : \implies {Area\ of\ rectangle\ =\ l\ \times\ b.}$

Here:-

• l, is for length = 2x.
• b, is for breadth = 3x.
• area is given as 150cm².

__________________

$\frak{\underline{\underline{\dag By\ substituting\ the\ values,\ we\ get:-}}}$

$\sf : \implies {Area\ of\ rectangle\ =\ l\ \times\ b} \\ \\ \\ \sf : \implies {150\ =\ 2x\ \times\ 3x} \\ \\ \\ \sf : \implies {150\ =\ 6x^2} \\ \\ \\ \sf : \implies {\cancel \dfrac{150}{6}\ =\ x^2} \\ \\ \\ \sf : \implies {25\ =\ x^2} \\ \\ \\ \sf : \implies {\sqrt{25}\ =\ x} \\ \\ \\ \sf : \implies {5\ =\ x} \\ \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf x\ =\ 5.}}}}\bigstar$

So here:-

$\sf : \implies {Length\ =\ 2x\ =\ 2\ \times\ 5\ =\ \bf 10cm.}$

$\sf : \implies {Breadth\ =\ 3x\ =\ 3\ \times\ 5\ =\ \bf 15cm.}$

Hence:-

$\sf \therefore {\underline{The\ required\ length\ is\ \bf 10cm.}}$