Question

*What is the length of a rectangle with an area of ​​108 sq.cm. and the sides are in the ration 4:3?*

1️⃣ 16 cm.
2️⃣ 12 cm.
3️⃣ 8 cm.
4️⃣ 15 cm.​

Answer 1

Appropriate Question :

• What is the length of a rectangle with an area of 108 sq.cm and there length and breadth are in the ratio 4:3 ?

AnswEr :

Given : The length and breadth of Rectangle are in Ratio 4:3 .

Need To Find : Length of Rectangle.

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❍ Let's Consider length and breadth of Rectangle be 4x and 3x respectively.

$\underline {\frak{\dag As \: We \:know\:that \::}}$

⠀⠀⠀⠀⠀ $\underline {\boxed {\sf{\star Area _{(Rectangle)} = l \times b \:sq.units .}}}$

⠀⠀⠀⠀⠀Here l is the Length of Rectangle in cm and b is the Breadth of Rectangle in cm . And we have given with the Area of Rectangle is 108 cm² .

⠀⠀⠀⠀⠀⠀$\underline {\bf{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$\qquad \qquad \qquad :\implies \tt{ 4x \times 3x =108cm^{2}}$

$\qquad \qquad \qquad :\implies \tt{ 12x^{2} =108cm^{2}}$

$\qquad \qquad \qquad :\implies \tt{ x^{2} =\dfrac{\cancel {108}}{\cancel {12}}}$

$\qquad \qquad \qquad :\implies \tt{ x^{2} =9 }$

$\qquad \qquad \qquad :\implies \tt{ x =\sqrt {9} }$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  x = 3\: cm}}}}\:\bf{\bigstar}$

Therefore,

• Length of Rectangle is 4x = 4 × 3 = 12 cm

• Breadth of Rectangle is 3x = 3 × 3 = 9 cm

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Length \:of\:Rectangle \:is\:12\: cm}}}$

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$\large {\boxed{\sf{\mid{\overline {\underline {\star Verification}}}\mid}}}$

$\underline {\frak{\dag As \: We \:know\:that \::}}$

⠀⠀⠀⠀⠀ $\underline {\boxed {\sf{\star Area _{(Rectangle)} = l \times b \:sq.units .}}}$

⠀⠀⠀⠀⠀Here l is the Length of Rectangle in cm and b is the Breadth of Rectangle in cm . And we have given with the Area of Rectangle is 108 cm² .

⠀⠀⠀⠀⠀⠀$\underline {\bf{\star\:Now \: By \: Substituting \: the \: Found \: Values \::}}$

$\qquad \qquad \qquad :\implies \tt{ 12 \times 9 =108cm^{2}}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  108cm^{2} = 108\: cm^{2}}}}}\:\bf{\bigstar}$

⠀⠀⠀⠀⠀$\therefore \underline {\bf{ Hence \:Verified}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

$\large {\boxed{\sf{\mid{\overline {\underline {\star More\:To\:know\::}}}\mid}}}$

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

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Answer 2

Answer:

12 cm

Step-by-step explanation:

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