A rectangle with diagonals of length 20cm has sides in the ratio 2 : 1 . find the area of the rectangle.
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A rectangle with diagonals of length 20cm has sides in the ratio 2 : 1 . find the area of the rectangle.
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A rectangle with diagonals of length 20cm has sides in the ratio 2 : 1 . find the area of the rectangle.
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[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \huge{ \sf{ \underline{ \underline \green{Question:- }}}}[/tex]
A rectangle with diagonals of length 20cm has sides in the ratio 2 : 1 . find the area of the rectangle.
Given:-
To find:-
[tex] \: \: \: \: \: \: \: \: \: \: \: \huge \sf{ \underline{ \underline{ \pink{Solution:- }}}}[/tex]
[tex] \: \: \: \: \: \huge{ \boxed{ \underline{ \mathfrak{ \red{By \: pythagoras \: theorem:-}}}}}[/tex]
[tex] \: \: \: \: \: \: \large \: : ⇰20² = (2x)² + (1x)² [/tex]
[tex] \: \: \: \: \red{ : ⇒400 = 4x² + 1x²}[/tex]
[tex] \: \: \: \: \: \: \pink{: ⇒ 400 = 5x²}[/tex]
[tex] \: \: \: \: \: \: \: \blue{\large \: : ⇒ x² = \frac{400}{5}}[/tex]
[tex] \: \: \: \: \: \: \red{ :⇒ x² = 80}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \orange{ :⇒ x =√80}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \sf \green{\: x = \sqrt{ x = 2×2×2×2×5}}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \:⇒ \large \: { \color{gold}{x = 4 \sqrt{5} }}[/tex]
[tex] \: \: \: \: \mathfrak{ \boxed{ \green{ \sf \: ∴length =2x = 2×4 \sqrt{5} = 8 \sqrt{5} }}}[/tex]
[tex] breadth = 1x= 4 \sqrt{5} [/tex]
⇒Area of a rectangle = l×b
[tex] \red{= 8 \sqrt{5} × 4 \sqrt{5} }[/tex]
[tex] \red{=32 ×5}[/tex]
[tex] \green{ = 160}[/tex]
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