Question

A rectangle with diagonals of length 20cm has sides in the ratio 2 : 1 . find the area of the rectangle.
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Answer 1

A rectangle with diagonals of length 20cm has sides in the ratio 2 : 1 . find the area of the rectangle.

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Answer 2

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$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \huge{ \sf{ \underline{ \underline \green{Question:- }}}}$

A rectangle with diagonals of length 20cm has sides in the ratio 2 : 1 . find the area of the rectangle.

Given:-

• Diagonals of length 20 cm.
• Ratio of sides are 2:1

To find:-

• Area of rectangle

$\: \: \: \: \: \: \: \: \: \: \: \huge \sf{ \underline{ \underline{ \pink{Solution:- }}}}$

• Let the length =2x
• and the breadth = 1x

$\: \: \: \: \: \huge{ \boxed{ \underline{ \mathfrak{ \red{By \: pythagoras \: theorem:-}}}}}$

$\: \: \: \: \: \: \large \: : ⇰20² = (2x)² + (1x)²$

$\: \: \: \: \red{ : ⇒400 = 4x² + 1x²}$

$\: \: \: \: \: \: \pink{: ⇒ 400 = 5x²}$

$\: \: \: \: \: \: \: \blue{\large \: : ⇒ x² = \frac{400}{5}}$

$\: \: \: \: \: \: \red{ :⇒ x² = 80}$

$\: \: \: \: \: \: \: \: \: \orange{ :⇒ x =√80}$

$\: \: \: \: \: \: \: \: \: \: \sf \green{\: x =  \sqrt{ x = 2×2×2×2×5}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:⇒ \large \: { \color{gold}{x = 4 \sqrt{5} }}$

$\: \: \: \: \mathfrak{ \boxed{ \green{ \sf \: ∴length =2x = 2×4 \sqrt{5} = 8 \sqrt{5} }}}$

$breadth = 1x= 4 \sqrt{5}$

⇒Area of a rectangle = l×b

$\red{= 8 \sqrt{5}  × 4 \sqrt{5} }$      

 $\red{=32 ×5}$

$\green{ = 160}$

Learn more:-

• Area of rectangle = length ×breadth
• Area of square =side ×side
• Area of triangle =½×b×h
• Area of circle =πr²