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?

Given, the length of the perpendiculars are 2 centimetres and 3 centimetres. Let us represent perpendicular sides as a and b and hypotenuse as c . According to hypotenuse theorem, a 2 + b 2 = c 2 Putting the value of a and b . ( 2 ) 2 + ( 3 ) 2 = c 2 2 + 3 = c 2 c 2 = 5 c = 5 Now we know the value of 2 = 1 . 41 , 3 = 1 . 73 , 5 = 2 . 24 . Adding 2 centimetres and 3 centimetres = 1 . 41 + 1 . 73 = 3 . 14 cm Difference between the sum of perpendicular sides and hypotenuse = 3 . 14 - 2 . 24 = 0 . 9 cm Hence, the sum of perpendicular side is larger by 0 . 9 cm than hypotenuse.

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?

Given, the length of the perpendiculars are 2 centimetres and 3 centimetres. Let us represent perpendicular sides as a and b and hypotenuse as c . According to hypotenuse theorem, a 2 + b 2 = c 2 Putting the value of a and b . ( 2 ) 2 + ( 3 ) 2 = c 2 2 + 3 = c 2 c 2 = 5 c = 5 Now we know the value of 2 = 1 . 41 , 3 = 1 . 73 , 5 = 2 . 24 . Adding 2 centimetres and 3 centimetres = 1 . 41 + 1 . 73 = 3 . 14 cm Difference between the sum of perpendicular sides and hypotenuse = 3 . 14 - 2 . 24 = 0 . 9 cm Hence, the sum of perpendicular side is larger by 0 . 9 cm than hypotenuse.

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 2>Q (5)

HARD

9th Kerala Board

IMPORTANT

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What is the hypotenuse of the right triangle with perpendicular sides $\sqrt{2}$ centimetres and $\sqrt{3}$ centimetres? How much larger than the hypotenuse is the sum of the perpendicular sides?

Important Questions on New Numbers

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,
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