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Answers
27)
Given that
Length of the rectangle = (l) = 40 cm
The length of the diagonal (d) = 41 cm
We know that
The length of a diagonal of a rectangle is √(l²+b²) units
Therefore, 41 = √(40²+b²)
=> 41² = 40²+b²
=> b² = 41²-40²
=> b² = 1681-1600
=> b² = 81
=> b = ±√81
=> b = ±9
Since the length of the side can't be negative.
Therefore, b = 9 cm
Now,
The perimeter of a rectangle = 2(l+b) units
=> P = 2(40+9)
=> P = 2(49)
=> P = 98 cm
Perimeter of the rectangle = 98 cm
28)
From the figure,
In ∆ ABC and In ∆ EDC
BC ≅ CD
∠ACB ≅ ∠ ECD
ECDAC ≅ CE
By SAS Congruency criterion
∆ ABC ≅ ∆ EDC
or
In ∆ ABC and ∆ABD
∠ABC ≅ ∠BAD
∠ACB ≅ ∠ BDA
By AA Congruency criterion
∆ABC ≅ ∆ BAD
29)
Given that
The money borrowed form the bank by Sanju
=(P) = Rs. 60000
Time (T) = 2 years
Rate of interest (R) = 8%
We know that
Simple Interest = PTR/100
On substituting these values in the above formula then
=> S.I. = (60000×2×8)/100
=> S.I. = 600×2×8
=> S.I = Rs. 9600
The interest is to be paid by Sanju is Rs. 9600
We know that
Amount = Principle + Simple Interest
=> A = 60000+9600
=> A = Rs. 69600
The amount has to be paid by Sanju in the given time is Rs. 69600
30)
Given that
The number of bad apples are mixed in the basket = 1
Let the number of good apples in the basket be X
Total number of apples in the basket initially = X+1
The percentage of bad apples = 25%
The percentage of good apples = 100-25 = 75%
Given that
The number of good apples in the basket now
= 30
Therefore,
75 % of total apples = 30
=> 75% of (X+1) = 30
=> 75%×(X+1) = 30
=> (75/100)×(X+1) = 30
=> (3/4)×(X+1) = 30
=> (X+1) = 30×4/3
=> X+1 = 10×4
=> X+1 = 40
Therefore, Total number of apples = 40
=> X = 40-1
=> X = 39
The number of good apples in the basket initially = 39
The number of bad apples in the basket initially
= 25% of 40
= (25/100)×40
=> (1/4)×40
=> 40/4
=> 10
The number of bad apples in the basket initially = 10
Now,
The ratio of the number of good apples to the number of bad apples
= 30:10
= 30/10
= 3:1
Answer:
27
Given that:
Length of the rectangle = (l) = 40 cm
The length of the diagonal (d) = 41 cm
We know that
The length of a diagonal of a rectangle is √(l²+b²) units
Therefore, 41 = √(40²+b²)
=> 41² = 40²+b²
=> b² = 41²-40²
=> b² = 1681-1600
=> b² = 81
=> b = ±√81
=> b = ±9
Since the length of the side can't be negative.
Therefore, b = 9 cm
Now,
The perimeter of a rectangle = 2(l+b) units
=> P = 2(40+9)
=> P = 2(49)
=> P = 98 cm
Perimeter of the rectangle = 98 cm
28)
From the figure,
In ∆ ABC and In ∆ EDC
BC ≅ CD
∠ACB ≅ ∠ ECD
ECDAC ≅ CE
By SAS Congruency criterion
∆ ABC ≅ ∆ EDC
or
In ∆ ABC and ∆ABD
∠ABC ≅ ∠BAD
∠ACB ≅ ∠ BDA
By AA Congruency criterion
∆ABC ≅ ∆ BAD
29)
Given that
The money borrowed form the bank by Sanju
=(P) = Rs. 60000
Time (T) = 2 years
Rate of interest (R) = 8%
We know that
Simple Interest = PTR/100
On substituting these values in the above formula then
=> S.I. = (60000×2×8)/100
=> S.I. = 600×2×8
=> S.I = Rs. 9600
The interest is to be paid by Sanju is Rs. 9600
We know that
Amount = Principle + Simple Interest
=> A = 60000+9600
=> A = Rs. 69600
The amount has to be paid by Sanju in the given time is Rs. 69600
30)
Given that
The number of bad apples are mixed in the basket = 1
Let the number of good apples in the basket be X
Total number of apples in the basket initially = X+1
The percentage of bad apples = 25%
The percentage of good apples = 100-25 = 75%
Given that
The number of good apples in the basket now
= 30
Therefore,
75 % of total apples = 30
=> 75% of (X+1) = 30
=> 75%×(X+1) = 30
=> (75/100)×(X+1) = 30
=> (3/4)×(X+1) = 30
=> (X+1) = 30×4/3
=> X+1 = 10×4
=> X+1 = 40
Therefore, Total number of apples = 40
=> X = 40-1
=> X = 39
The number of good apples in the basket initially = 39
The number of bad apples in the basket initially
= 25% of 40
= (25/100)×40
=> (1/4)×40
=> 40/4
=> 10
The number of bad apples in the basket initially = 10
Now,
The ratio of the number of good apples to the number of bad apples
= 30:10
= 30/10
= 3:1
Step-by-step explanation:
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