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If a diagonal of a rectangle is twice its larger side, then its length and breadth are in the ratio of____?
Assume that the length of the smaller side of the rectangle BC = x
Length of the larger side AB = y
It is given that the length of the diagonal is two times that of the larger side.
Diagonal of the rectangle AC = 2y
By using Pythagoras theorem
By substituting the values
On further calculation
We get
By taking square roots of both sides,
Hence, the ratio of the larger side to the smaller side is 1: .
The dimensions of a rectangle are such that the length is thrice the width. If the length of the diagonal is \(8\surd 10\;\)m, then the perimeter of the rectangle is?
Consider ABCD as a rectangle.
Assume that the width of the rectangle BC = x m
We know that the length is three times width of the rectangle.
So, length of the rectangle AB = 3x m
AC is the diagonal of rectangle
Consider ABC as a rightangled triangle.
By substituting the values
We get
On further calculation
x = = 8 m
So, the breadth of the rectangle x = 8 m
Length of the rectangle 3x = 3 8 = 24 m
Perimeter = 2 (Length + Breadth)
By substituting the values
Perimeter = 2 (24 + 8) = 2 32 = 64 m
If 12 men can do a piece of work in 18 days, in how many days will 8 men complete it?
Let the required number of days be x
8:12::18:x
Find the third proportional of 16 and 20.
Let the third proportional of 16 and 20 be x.
Then 16, 20, x are in proportion.
This means 16 : 20 = 20 : x
So, 16x = 20 20
x = = 25
Therefore, the third proportional of 16 and 20 is 25.
The ratio of number of boys and girls is 4 : 3. If there are 18 girls in a class, find the number of boys in the class and the total number of students in the class.
Number of girls in the class = 18
Ratio of boys and girls = 4 : 3
According to the question,
Therefore, total number of students = 24 + 18 = 42
The first, second and third terms of the proportion are 42, 36, 35. Find the fourth term.
Let the fourth term be x.
Thus 42, 36, 35, x are in proportion.
Product of extreme terms = 42 x
Product of mean terms = 36 35
Since, the numbers make up a proportion
Therefore, 42 x = 36 35
or, x =
or, x = 30
Therefore, the fourth term of the proportion is 30.
Divide ₹370 into three parts such that second part is 1/4 of the third part and the ratio between the first and the third part is 3 : 5. Find each part.
Let the first and the third parts be 3x and 5x.
Second part = of third part.
=
Therefore, 3x + + 5x = 370
Therefore, first part = 3x
= 3 × 40
= ₹120
Second part =
= =₹50
Third part = 5x
= 5 × 40
=₹ 200
Mother divided the money among Ron, Sam and Maria in the ratio 2 : 3 : 5. If Maria got ₹150, find the total amount received by Ron, Maria and Sam.
Let the money received by Ron, Sam and Maria be 2x, 3x, 5x respectively.
Given that Maria has got ₹150.
Therefore, 5x = 150
or, x =
or, x = 30
So, Ron got = 2x
= ₹ 2 30 = ₹60
Sam got = 3x
= 3 60 = ₹90
Therefore, the total amount ₹ (60 + 90 + 150) = ₹300
The length of the ribbon was originally 30 cm. It was reduced in the ratio 5 : 3. What is its length now?
Length of ribbon originally = 30 cm
Let the original length be 5x and reduced length be 3x.
But 5x = 30 cm
x = cm = 6 cm
Therefore, reduced length = 3 cm
= 3 × 6 cm = 18 cm
What must be added to each term of the ratio 2 : 3, so that it may become equal to 4 : 5?
Let the number to be added be x, then (2 + x) : (3 + x) = 4 : 5
If 2A = 3B = 4C, find A : B : C
Let 2A = 3B = 4C = x
So, A = ,B = ,C =
The L.C.M of 2, 3 and 4 is 12
Therefore, A : B : C = 12 : 12 :
= 6x : 4x : 3x
= 6 : 4 : 3
Therefore, A : B : C = 6 : 4 : 3
The first, second and fourth terms of a proportion are 16, 24 and 54 respectively. The third term is
Consider x as the third term
We can write it as
16: 24 = x: 54
So, we get
By cross multiplication
If a, b, c are in proportion, then
We know that a, b, c are in proportion
So we get a: b :: b: c
12 men can finish a piece of work in 25 days. The number of days in which the same piece of work can be done by 20 men, is
Consider x days required by 20 men to do the same work
So, we get,
= 15 days
If a, b, c, d are in proportion, then
It is given that a, b, c, d are in proportion
We can write it as a : b :: c : d
So, we get
By cross multiplication
ad = bc
If 4, a, a, 36 are in proportion, then a =
It is given that 4, a, a, 36 are in proportion
We can write it as 4 : a :: a : 36
So, we get
By cross multiplication
We get,
So, a = 12
Length and width of a field are in the ratio 5 : 3. If the width of the field is 42 m, then its length is
It is given that length and width of a field = 5: 3
Consider x m as the length
Width of the filed = 42 m
So, the length can be written as
By cross multiplication
3x = 42 × 5 = 210
By division
x = = 70m
Two numbers are in the ratio 7 : 9. If the sum of the numbers is 112, then the larger number is?
Consider x as the largest number
So, we get
7x + 9x = 112
16x = 112
x = = 7
Here
7x = 7 × 7 = 49
9x = 9 × 7 = 63
Hence, the largest number is 63.
The ratio of story books in a library to other books is 1: 7. The total number of story books is 800. Find the total number of books in the library.
It is given that
Ratio of story books in a library to other books = 1: 7
Consider the ratio as x
So, the number of story books = x
Number of other books = 7x
We know that
Total number of story books = 800
Number of other books = 7 × 800 = 5600
Total number of books = 5600 + 800 = 6400
Hence, the total number of books in the library is 6400
The angles of a triangle are in the ratio 1: 3: 2. The measure of the largest angle is
We know that the sum of all the angles = 180°
So, the largest angle == 90°