(F) The hypotenuse of a right-angled triangle is 34 cm . If one side is 30 cm long, then the other side is
(a) 4 cm
(b) 8 cm
(c) 16 cm
(d) 64 cm
GIVE THE SOLUTION
Answers
given one side = 30 cm
let the other side of right angle be ' x '
according to Pythagoras Theorem,
( hypotenuse)^2 = sum of the squares of other two sides of right angle triangle
( 34 )^2 = ( 30 )^2 + ( x)^2
1156 = 900 + x^2
x^2 = 256 => x = √256
x = 16 cm
other side of triangle = 16 cm
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Q.(d): let the number be ' x '
express 2 /3 of x:
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2 / 3 of x = 2x/ 3
express 1 /3 of x:
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1/ 3 of x = x / 3
according to question,
(x / 3) + 3 = 2x / 3
3 (x + 9 ) = 3 ( 2x )
3x + 27 = 6x
3x = 27 => x = 9
required number = 9
thus , option (ii) is correct.
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Q.(e) : let the present age of B be 'x '
present age of B = x yrs
present age of A = ( x + 15 ) yrs
10 years ago :
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age of B = ( x - 10 ) yrs
age of A = (x + 15 ) - 10 =( x + 5 ) yrs
since , 10 years ago age of A was 4 times of B' s age ,
(x + 5 ) = 4 × ( x - 10 )
x + 5 = 4x - 40
3x = 45. =. x = 15
Answer:
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present age of A= x + 15 = 15 + 15
= 30yrs
option (iii) is the correct answer.
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(d)
Let the number be x.
According to the question,
⇒ (2/3)x = (1/3)x + 3
⇒ (2/3)x - (1/3)x = 3
⇒ (2x - x)/3 = 3
⇒ x/3 = 3
⇒ x = 9.
Therefore, the number is 9.
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(e)
Let the age of b be x.
Then, the age of A = x + 15.
10 years ago:
⇒ Age of A = x + 15 - 10 = x + 5.
⇒ Age of B = x - 10.
According to question,
⇒ (x + 5) = 4(x - 10)
⇒ x + 5 = 4x - 40
⇒ 3x = 45
⇒ x = 15.
Then, the age of A = 15 + 5 = 20.
Therefore,
⇒ Age of A = 30 years
⇒ Age of B = 15 years.
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(f)
Given hypotenuse = 34 cm.
Let one side be x.
Then the other side be x + 30 cm.
By Pythagoras theorem, we get
⇒ x^2 + (30)^2 = (34)^2
⇒ x^2 + 900 = 1156
⇒ x^2 = 1156 - 900
⇒ x^2 = 256
⇒ x = 16,-16{It cannot be negative}
⇒ x = 16 cm.
Therefore, the length of the other side is 16 cm.
Hope it helps!