Question

diagonal of a rectangle is 17cm and the perimeter is 46cm. the area of rectangle will be :

Answer 1

Length of rectangle = l 
Breadth of rectangle = b

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Perimeter = 2( l+ b) 
          46 = 2( l+ b) 
          23 =  l + b   ------1equation


Given that diagonal = 17 cm

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BY PYTHAGORAS THEOREM,[length&breadth are perpendicular to each other]
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So,

l² + b² = 17²

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(a + b)² = a² + b² + 2ab 
(a + b)² - 2ab = a² + b²
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(l + b)² - 2lb = 289 

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On Putting the value of ( l + b) from 1equation, we get
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(23)² - 2lb =  289

529 - 2lb = 289 

529 - 289 = 2lb 

240 = 2lb 

120 = lb 

120 = length × breadth     ----2equation

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Area of rectangle = length × breadth

From 2equation, we get that length × breadth 

Area of rectangle = length × breadth 
                             = 120 cm²