plz solve the question with explanation...
Answers
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1 )
Let the breadth be x .
Length = 2 x
Perimeter will be the same .
Let radius be r .
2 ( 2 x + x ) = 2 π r
⇒ 6 x = 2 π r
⇒ π r = 3 x
⇒ r = 3 x / π ..... ( 1 )
Area of circle = π r²
Area of rectangle = 2 x × x = 2 x²
2 x² - 104.5 = π r²
But r = 3 x / π
Hence :
2 x² - 104.5 = π ( 9 x²/π² )
⇒ 2 x² - 104.5 = 9x²/π
⇒ π ( 2 x² - 104.5 ) = 9 x²
⇒ 44/7 x² - 1045/10 × 22/7 = 9 x²
⇒ 44 x² - 1045/10 × 22 = 63 x²
⇒ 19 x² = 1045/10 × 22
⇒ x² = 55/10 × 22
⇒ x² = 11 × 5 × 11 × 2/10
⇒ x² = 121
⇒ x = 11
Now length of wire = 2 ( 2 x + x ) = 6 x
= 66 cm
ANSWER :
66 cm
2 )
18 balls are there,
x are red .
18 - x are not red .
P ( not red ) = ( 18 - x ) / 18
⇒ 1 - x/18
2 more red balls are put .
Total balls = 20
Red balls = 2 + x
P = 9/8 ( x )/18
= ( x )/16
Probability = ( 2 + x )/20
So : ( 2 + x ) / 20 = x / 16
= 16 ( 2 + x ) = 20 x
= 4 ( 2 + x ) = 5 x
= 8 + 4 x = 5 x
= x = 8