Q6 Using Euclid's algorithm , find HCF of 4052 and 12576. (3)
Q7 An A.P. consists of 50 terms of which 3rd term is 12 and last term is 106 .Fnd 29th term (3)
Q8 Prove that √7 is an irrational number. (3)
Q9 The diagonal of a rectangular field is 16 more than the shorter side. If the longer side is 30 more than the
Shorter side.Find the area of field.
Answers
Answer:
Answer:solution:-6
HCF of 4052 and 12576 by Long Division
Step 1: Divide 12576 (larger number) by 4052 (smaller number). Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (4052) by the remainder (420). Step 3: Repeat this process until the remainder = 0.
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solution:-7
Therefore, 29th term is 64.
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solution:-8
Given √7
To prove: √7 is an irrational number.
Proof:
Let us assume that √7 is a rational number.
So it t can be expressed in the form p/q where p,q are co-prime integers and q≠0
√7 = p/q
Here p and q are coprime numbers and q ≠ 0
Solving
√7 = p/q
On squaring both the side we get,
=> 7 = (p/q)2
=> 7q2 = p2……………………………..(1)
p2/7 = q2
So 7 divides p and p and p and q are multiple of 7.
⇒ p = 7m
⇒ p² = 49m² ………………………………..(2)
From equations (1) and (2), we get,
7q² = 49m²
⇒ q² = 7m²
⇒ q² is a multiple of 7
⇒ q is a multiple of 7
Hence, p,q have a common factor 7. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number
√7 is an irrational number.
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Solution :-9
Let the length of shorter side be x m.
Length of diagonal = (x + 16) m
And the length of longer side = (x + 14) m.
According to the Question,
Using Pythagoras theorem,
⇒ x² + (x + 14)² = (x + 16)²
⇒ x² - 4x - 60 = 0
⇒ x² + 6x - 10x - 60 = 0
⇒ x(x + 6) - 10(x + 6) = 0
⇒ (x + 6) (x - 10) = 0
⇒ x = - 6, 10 (As x can't be negative)
⇒ x = 10 m
Hence, the length of sides are 10 m and 24 m.
Answer:
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