Of four equal equilateral triangles, two cut vertically into halves and two whole are put together to make a rectangle, as shown below, , If a side of the equilateral triangle is 1 m , what is the area and perimeter of the rectangle?

Given that, Side of the equilateral triangle is 1 m And cut the triangle into halves as shown, Using Pythagoras theorem, Sides of the triangles are 1 m , 3 2 m , 1 2 m Now the rectangle is as given, Hence,length of rectangle is 3 2 + 3 2 = 3 m Width of rectangle is 1 m Perimeter of rectangle = 2 length + width = 2 1 + 3 = 2 + 2 3 3 ≈ 1 . 73 So,the perimeter of rectangle = 2 + 2 × 1 . 73 = 5 . 46 m Area of rectangle = length × width = 3 × 1 = 3 = 1 . 73 m 2 .

From the pairs of numbers given as 3 , 12 , check whether the product is a natural number or a fraction.

We need to check the product of the given number as , 3 , 12 . We know that, Product of a , b is a × b = ab Hence,the product of the numbers 3 , 12 is 3 × 12 = 12 × 3 = 36 = 6 Therefore,the product of 3 , 12 is 6 a natural number.

From the pairs of numbers given as 3 , 1 . 2 , check whether the product is a natural number or a fraction.

We need to check the product of the given number as , 3 , 1 . 2 . We know that, Product of a , b is a × b = ab Hence,the product of the numbers 3 , 1 . 2 is 3 × 1 . 2 = 1 . 2 × 3 = 3 . 6 Therefore,the product of 3 , 1 . 2 is 3 . 6 neither a natural number nor a fraction.

From the pairs of numbers given as 5 , 8 , check whether the product is a natural number or a fraction.

We need to check the product of the given number as , 5 , 8 . We know that, Product of a , b is a × b = ab Hence,the product of the numbers 5 , 8 is 5 × 8 = 5 × 8 = 40 Therefore,the product of 5 , 8 is neither a natural number nor a fraction.

From the pairs of numbers given as 0 . 5 , 8 , check whether the product is a natural number or a fraction.

We need to check the product of the given number as , 0 . 5 , 8 . We know that, Product of a , b is a × b = ab Hence,the product of the numbers 0 . 5 , 8 is 0 . 5 × 8 = 4 = 2 Therefore,the product of 0 . 5 , 8 is a natural number.

From the pairs of numbers given as 7 1 2 , 3 1 3 , check whether the product is a natural number or a fraction.

We need to check the product of the given number as , 7 1 2 , 3 1 3 . We know that, Product of a , b is a × b = ab Hence,the product of the numbers 7 1 2 × 3 1 3 = 15 2 × 10 3 = 25 = 5 Therefore,the product of 7 1 2 , 3 1 3 is a natural number.

E M B I B E

Standard 9 Mathematics Part - 1>Chapter 4 - New Numbers>Exercise 3

Kerala Board Solutions for Chapter: New Numbers, Exercise 3: Exercise 3

Author:Kerala Board

Kerala Board Mathematics Solutions for Exercise - Kerala Board Solutions for Chapter: New Numbers, Exercise 3: Exercise 3

Attempt the free practice questions on Chapter 4: New Numbers, Exercise 3: Exercise 3 with hints and solutions to strengthen your understanding. Standard 9 Mathematics Part - 1 solutions are prepared by Experienced Embibe Experts.

Questions from Kerala Board Solutions for Chapter: New Numbers, Exercise 3: Exercise 3 with Hints & Solutions

EASY

9th Kerala Board

IMPORTANT

Standard 9 Mathematics Part - 1>Chapter 4 - New Numbers>Exercise 3>Q (1)

Of four equal equilateral triangles, two cut vertically into halves and two whole are put together to make a rectangle, as shown below,
Question Image ,
If a side of the equilateral triangle is $1 m$ , what is the area and perimeter of the rectangle?

MEDIUM

9th Kerala Board

IMPORTANT

Standard 9 Mathematics Part - 1>Chapter 4 - New Numbers>Exercise 3>Q (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,
Question Image , ,
If the side of the square is $2 cm$ , what is the perimeter and area of the trapezium?