[tex]\huge{\color{Silver}{\underline{\color{blue}{\underline{ \color{beige} {\underline{\color{ruby} {\textbf{\textsf{\colorbox{Teal}{♕♡ ᗅᘉSᙎᙍᖇ ♡♕:-}}}}}}}}}}}[/tex]
[tex]\huge{----------------}[/tex]
[tex]\boxed{\color{Teal}{\mathfrak{Given,}}}[/tex]
Area of Rectangle = 90% of Area of Square
It is given that Area of Rectangle = 360 cm²
[tex]\boxed{\color{Darkorchid}{\mathfrak{To \:Find,}}}[/tex]
Length of each side of the square.
[tex]\boxed{\color{Aqua}{\mathfrak{Proof,}}}[/tex]
From given,
360 cm² = [tex]\frac{90}{100}[/tex] × Area of Square
→→ Area of Square = [tex]\frac{100}{90}[/tex] × 360 cm²
→→ Area of Square = 100 × 4 cm²
→→ Area of Square = 400 cm² → (1)
Now,
[tex]\boxed{Area\:of\:a\:Square = s^{2} \:square\:units - \:where\:s\: is \:the\:side\:of\:the\:square}[/tex]
Now, Substituting the formula in (1), we get,
s² square units (or) s² units² = 400 cm²
s units = √400 cm
s (side) = 20 cm
[tex]\huge{\color{Gold}{\underline{\color{blue}{\underline{ \color{Darkorchid} {\underline{\color{ruby} {\textbf{\textsf{\colorbox{Aqua}{✅ ᏗᏁᏕᏇᏋᏒ ᏰᎽ ᏉᎥᏁᎧᏟᏂᏗᏁ✅}}}}}}}}}}}[/tex]
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Verified answer
Given :
Solution Explanation :
[tex]Area \: of \: rectangle = 90\% \\ of \: the \: area \: of \: a \: square \\ \\ 360 = \frac{90}{100} \times {a}^{2} \\ \\ \frac{360 \times 100}{90} = {a}^{2} \\ \\ \frac{{\cancel{360} \times 100}}{{\cancel{90}}} = {a}^{2} \\ \\ 4 \times 100 = {a}^{2} \\ \\400 = {a}^{2} \\ \\ a = \sqrt{400} \\ \\ a = \sqrt{20 \times 20} \\ \\ a = 20 \: cm[/tex]
[tex]\huge{\color{Silver}{\underline{\color{blue}{\underline{ \color{beige} {\underline{\color{ruby} {\textbf{\textsf{\colorbox{Teal}{♕♡ ᗅᘉSᙎᙍᖇ ♡♕:-}}}}}}}}}}}[/tex]
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[tex]\huge{----------------}[/tex]
[tex]\boxed{\color{Teal}{\mathfrak{Given,}}}[/tex]
Area of Rectangle = 90% of Area of Square
It is given that Area of Rectangle = 360 cm²
[tex]\boxed{\color{Darkorchid}{\mathfrak{To \:Find,}}}[/tex]
Length of each side of the square.
[tex]\boxed{\color{Aqua}{\mathfrak{Proof,}}}[/tex]
From given,
Area of Rectangle = 90% of Area of Square
360 cm² = [tex]\frac{90}{100}[/tex] × Area of Square
→→ Area of Square = [tex]\frac{100}{90}[/tex] × 360 cm²
→→ Area of Square = 100 × 4 cm²
→→ Area of Square = 400 cm² → (1)
Now,
[tex]\boxed{Area\:of\:a\:Square = s^{2} \:square\:units - \:where\:s\: is \:the\:side\:of\:the\:square}[/tex]
Now, Substituting the formula in (1), we get,
s² square units (or) s² units² = 400 cm²
s units = √400 cm
s (side) = 20 cm
∴ The Length of the side of the square is 20 cm.
[tex]\huge{----------------}[/tex]
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[tex]\huge{\color{Gold}{\underline{\color{blue}{\underline{ \color{Darkorchid} {\underline{\color{ruby} {\textbf{\textsf{\colorbox{Aqua}{✅ ᏗᏁᏕᏇᏋᏒ ᏰᎽ ᏉᎥᏁᎧᏟᏂᏗᏁ✅}}}}}}}}}}}[/tex]