Answer :
[tex] \bigstar \: \bf \underline{ \boxed{ \bf Answer:}} \: \bigstar[/tex]
[tex]\maltese\:{\underline{\boxed{\bf{L = 20\:ft\;\;\;and\;\;\;B = 10\:ft}}}\:\maltese}[/tex]
[tex] \bigstar \: \bf \underline{ \boxed{ \bf Explanation:}} \: \bigstar[/tex]
It is given that,
- Area of rectangle = 200ft square
- Length = 2 × Breadth
We need to find,
- Length and breadth of rectangle = ???
Formula to be used,
- [tex]\bf{A_{(Rect)} = L \times B}[/tex]
Let's find the length and breadth of rectangle :
Substituting the values in the formula, we get :
[tex]: \implies\sf{200 = 2B \times B}[/tex]
[tex]: \implies\sf{200 = 2B^2}[/tex]
[tex]: \implies\sf{B^2 = \cancel{\dfrac{200}{2}}}[/tex]
[tex]: \implies\sf{B^2 = 100}[/tex]
[tex]: \implies\sf{B = \sqrt{100}}[/tex]
[tex]: \implies\bf{B = 10\:ft}[/tex]
According to the question,
- Length = 2 × Breadth
[tex]: \implies\sf{L = 2 \times 10}[/tex]
[tex]: \implies\bf{L = 20\:ft}[/tex]
Hence,
- [tex]\underline{\boxed{\bf{L = 20\:ft\;\;\;and\;\;\;B = 10\:ft}}}[/tex]
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[tex]\rm\: More\: Information:[/tex]
[tex]\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\pmb{{More \: formulas}}} \\ \\ \bigstar \rm{{A_{(\bigcirc)}} = \pi r^{2}}\\ \\ \bigstar \rm{{P_{(\bigcirc)}} = 2\pi r} \\ \\ \bigstar \rm {{A_{(\square)}} = Side^{2}} \\ \\ \bigstar \rm{{P_{(\square)}} = 4\times Side} \\ \\ \bigstar \rm{{A_{(Rect)}} = L \times B} \\ \\ \bigstar \rm{{P_{(Rect)}} = 2(L + B)} \\ \\ \bigstar \rm{{P_{(\parallel^{gm})}} = 2(L + B)} \\ \\ \bigstar \rm{{A_{(\parallel^{gm})}} = Base \times Height} \\ \\ \bigstar \rm{{P_{(\triangle)} = A + B + C}} \\ \\ \bigstar \rm{{A_{(\triangle)}} = \dfrac{Base \times Height}{2}} \\ \\ \bigstar \rm{{A_{(Rhombus)}} = \dfrac{1}{2} \times {D_{1}} \times {D_{2}}} \\ \\ \bigstar \rm{{P_{(Rhombus)}} = 2\sqrt{D_{1}^{2}} + \sqrt{D_{2}^{2}}} \\ \\ \bigstar \rm{{A_{(Trapezium)}} = \dfrac{Sum\:of\:\parallel\:sides \times Height}{2}} \\ \\ \bigstar \rm{{P_{(Trapezium)}} = AB + BC + CD + DA}\:\end{array} }}\end{gathered}[/tex]