Kerala Syllabus 9th Standard Maths Solutions Chapter 4 New Numbers
Kerala Syllabus 9th Standard Maths Solutions Chapter 4 New Numbers
Kerala State Syllabus 9th Standard Maths Solutions Chapter 4 New Numbers
Kerala Syllabus 9th Standard Maths New Numbers Text Book Questions and Answers
Textbook Page No. 49
New Numbers Class 9 Kerala Syllabus Chapter 4 Question 1.
In the picture, the square on the hypotenuse of the top most right triangle is drawn. Calculate the area and the length of a side of the square.
Answer:
Class 9 Maths Chapter 4 Kerala Syllabus Question 2.
A square is drawn on the altitude of an equilateral triangle of side 2m
(i) What is the area of the square?
(ii) What is the altitude of the triangle?
iii) What are the lengths of the other two sides of the triangle shown below?
Answer:
(i)
(ii) Height of triangle √3cm
(iii)
Kerala Syllabus 9th Standard Maths Chapter 4 Question 3.
We have seen in Class 8 that any odd number can be written as the difference of two perfect squares. (The lesson, Identities). Using this, draw squares of areas 7 and 11 square centimetres.
Answer:
3² – 2² = 5
4² – 3² = 7
5² – 4² = 9
n² – (n – 1)² = 2n – 1
so 4² – 3² = 7
6² – 5² = 11
Draw a right angled triangle with hypotenuse 4cm and one of its side as 3 cm. It’s one side is √7 cm
Draw square BCDE with BC as the side.
Area of square BCDE = √7× √7 = 7 sq.cm
Draw a right angled triangle with hypotenuse 6 cm and one of its side as 5 cm. It’s one side is 1–√1 cm
Draw square BCDE with BC as the side.
Area of square QRST = √11 × √11 = 11 sq.m
Class 9 Maths Chapter 4 New Numbers Kerala Syllabus Question 4.
Explain two different methods of drawing a square of area 13 square centimetres.
Answer:
Method 1
72 – 62 = 13 Draw a right angled triangle with one side 6 cm and hypotenuse 7 cm.
Draw square QRST with QR as the side.
Method 2.
9th Standard Maths Chapter 4 Kerala Syllabus Question 5.
Find three fractions larger than √2 and less than √3
Answer:
Textbook Page No. 52
Kerala Syllabus 9th Standard Maths Notes Chapter 4 Question 1.
The hypotenuse of a right triangle is 112 m and another side is 12 m. Calculate its perimeter correct to a centimetre.
Answer:
Square of the third side is =
New Numbers Class 9 Questions And Answers Kerala Syllabus Chapter 4 Question 2.
The picture shows an equilateral triangle cut into halves by a line through a vertex.
i. What is the perimeter of a part? (See the second problem at the end of the previous section)
ii. How much less than the perimeter of the whole triangle is this?
The sides of the new triangle is 2 cm,
1 m, √22−12 m
(i) Perimeter of one of the triangle =
2 + 1 +√3= 3 + 1.73 = 4.73 m
(ii) Perimeter of the whole triangle
= 2 + 2 + 2 = 6m
Less in the perimeter
= 6 – 4.73 = 1.27m
9th Class Maths Notes Chapter 4 Kerala Syllabus Chapter 4 Question 3.
Calculate the perimeter of the triangle shown below
Answer:
Draw BD perpendicular to AC
9th Maths Kerala Syllabus Chapter 4 Question 4.
We have seen how we can draw a series of right triangles as in the picture.
(i) What are the lengths of the sides of the tenth triangle drawn like this?
(ii) How much more is the perimeter of the tenth triangle than the perimeter of the ninth triangle?
(iii) How do we write in algebra, the difference in perimeter of the n‘h triangle and that of the triangle just before it?
Answer:
(ii) Perimeter of tenth triangle
iii. Sides of the nth triangle are
Maths 9th Kerala Syllabus Chapter 4 Question 5.
What is the hypotenuse of the right triangle with perpendicular sides 2–√ centimetres and 3–√ centimetres? How much larger than the hypotenuse is the sum of the perpendicular sides?
Answer:
= (1.73 + 1.41) – 2.24 = 3.14 – 2.24 cm = 0.9
Textbook Page No. 57
Class 9 Maths Kerala Syllabus Chapter 4 Question 1.
Of four equal equilateral triangles, two cut vertically into halves and two whole are put together to make a rectangle.
Perimeter = 1 +√3/2 + √3/2 + 1 + √3/2 + √3/2
= 2 + 2√3 m
Area of the rectangle = 1 × √3 = √3 m²
Class 9 Maths Kerala Syllabus Chapter 4 Question 2.
A square and an equilateral triangle of sides twice as long are cut and the pieces are rearranged to form a trapezium, as shown below:
If a side of the square is 2 cm, what are the perimeter and area of the trapezium?
9th Maths Notes Kerala Syllabus Chapter 4 Question 3.
Calculate the perimeter and area of the triangle in the picture.
Answer:
Draw a perpendicular from B to AC
AB = 4cm
AD = 2
Kerala Syllabus 9th Standard Maths Notes Pdf Chapter 4 Question 4.
From the pairs of numbers given below, pick out those whose product is a natural number or a fraction.
product is natural number
Textbook Page No. 60
9th Standard Maths Notes Kerala Syllabus Chapter 4 Question 1.
Calculate the length of the sides of the equilateral triangle on the right, correct to a millimetre.
Question 2.
Question 3.
Question 4.
Question 5.
Question 6.
All red triangles in the picture are equilateral. What is the ratio of the sides of the outer and inner squares?
Kerala Syllabus 9th Standard Maths New Numbers Exam Oriented Text Book Questions and Answers
Question 1.
Find the perimeter of the given triangle.
Question 2.
Find the perimeter of the rectangle with area 10 sq. centimetres.
Answer:
Let one side of the reactable be ‘a’
Question 3.
Question 4.
Question 5.
Question 6.
Question 7.
Find the perimeter of the triangle correct to two, decimal places.
Question 8.
Question 9.
Question 10.
Question 11.
Question 12.
Simplify the following.
Question 13.
Simplify the following.
Question 14.
Question 15.
Question 16.
Question 17.
In the figure given below, PQRS is a square of each side is 3 cm. Each sides of the square is divided into 3 equal parts. Joining these points to get an octagon, find its perimeter.
Answer:
ΔAPH is a right angled triangle.
AP = PH = 1 cm
Question 18.
The three points lie on a straight line.
Question 19.
Question 20.
Find the sum 745+7180+780
Answer:
Question 21.
A, B, C are three points such that AB = √50 cm, BC = √98 cm, AC =
√288 cm. Do they lie on a straightline?
Answer:
If A, B, C are points on the same line then AB + BC = AC
Here AB + BC = AC. So the three given points are on the same straight line.
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