Question

1. Define rational number. Give 2 examples.

2. Write the divisibility test steps for 2, 3 and 11.

3. Construct 3x3 magic square (numbers from 1 to 9)

4. Solve: A triangle having a perimeter 56 and its sides are 2x, 2x+3, 2x+5 find

the respective length of the sides of the triangle?​

Answer 1

Answer: 1.A rational number is a number that can be expressed as a fraction where both the numerator and the denominator in the fraction are integers. The denominator in a rational number cannot be zero. Expressed as an equation, a rational number is a number a/b, b≠0.

2.Divisibility Test for 2: If, the last digit of a given number is divisible by 2 then the given number itself is also divisible by 2.

Divisibility Test for 3: Suppose, we are given a large number and we want to check if that particular given number is divisible by 3. We sum up all the digits of number. If, sum of all the digits is divisible by 3 then the number itself is also divisible by 3.

Divisibility Test for 11: Just understand divisibility test of 11 by example. Suppose, we want to check if the number 14641 is divisible by 11 or not.

3.Magic squares have grown in popularity with the advent of mathematics-based games like Sudoku. A magic square is an arrangement of numbers in a square in such a way that the sum of each row, column, and diagonal is one constant number, the so-called "magic constant." This article will tell you how to solve any type of magic square, whether odd-numbered, singly even-numbered, or doubly-even numbered.

4.Given :-

Sides of triangle

2x

2x + 3

2x + 5

Perimeter - 56

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To Find :-

Length of each side

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Solution :-

( we know that, perimeter = sum of all sides )

So,

2x + 2x + 3 + 2x + 5 = 56

6x + 8 = 56

6x = 56 - 8

6x = 48

x = 48/6

x = 8

Finding length of each side :-

2 x 8 = 16 cm

2 ( 8 ) + 3 = 19 cm

2 ( 8 ) + 5 = 21 cm

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Verification :-

16 + 19 + 21 = 56