GSEB Class 6 Maths Solutions Chapter 11 Algebra Exercise 11.2

Question 1. The side of an equilateral triangle is shown by \( l \). Express the perimeter of the equilateral triangle using \( l \).
Answer:The side of the equilateral triangle ABC is \( l \). Therefore, its perimeter equals AB plus BC plus AC. This gives us \( l + l + l = 3l \). Thus, the perimeter of an equilateral triangle becomes \( 3l \). Note: \( 3 \times l \), 3.1, and \( 3l \) all mean the same thing. They show the multiplication of 3 and \( l \).
In simple words: An equilateral triangle has three equal sides, each measured as \( l \). To find the perimeter, you just add the lengths of all three sides together. So, \( l + l + l \) becomes \( 3l \), which is the total distance around the triangle.

Exam Tip: Remember that an equilateral triangle has three sides of equal length. Its perimeter is always found by multiplying the side length by three.

Question 2. The side of a regular hexagon in the figure is denoted by \( l \). Express the perimeter of the hexagon using \( l \).
Answer:Hint: A regular hexagon has all six of its sides the same length. Since all sides of a regular hexagon possess equal lengths, each side of the hexagon is \( l \). Therefore, its perimeter is \( l + l + l + l + l + l = 6l \).
In simple words: A regular hexagon has six sides, all the same length. If each side is \( l \), then its perimeter is found by adding \( l \) together six times, which gives you \( 6l \).

Exam Tip: Always remember that the perimeter of any regular polygon is found by multiplying the number of sides by the length of one side.

Question 3. A cube is a three-dimensional figure as shown here. It has six faces and all of them are identical squares. The length of an edge of the cube is given by \( l \). Find the formula for the total length of the edges of a cube.
Answer:A cube possesses six identical faces and contains 12 edges. Every edge has an equal length. So, the total length of all edges equals \( 12 \times l \) or simply \( 12l \).
In simple words: A cube has 12 edges, and they all have the same length. If one edge is \( l \), then to find the total length of all edges, you multiply \( l \) by 12.

Exam Tip: For problems involving 3D shapes, count the number of edges carefully to avoid errors in your calculations.

Question 4. The diameter of a circle is a line that joins two points on the circle and also passes through the centre of the circle. (In the adjoining figure, AB is the diameter of the circle; C is its centre.) Express the diameter of the circle (d) in terms of its radius (r).
Answer:The radius is represented by \( r \) and the diameter by \( d \). Because the diameter of a circle is twice the radius. Consequently, the diameter equals 2 times the radius. This means \( d = 2 \times r \) or just \( d = 2r \).
In simple words: The diameter of a circle is simply two times its radius. So, if you know the radius \( r \), you just multiply it by 2 to get the diameter \( d \).

Exam Tip: Remember the basic relationships in a circle: diameter is twice the radius, and the radius is half the diameter. These are fundamental for solving circle-related problems.

Question 5. To find the sum of three numbers 14, 27, and 13 we can have two ways: (a) We may first add 14 and 27 to get 41 and then add 13 to it to get the total sum of 54 or (b) We may add 27 and 13 to get 40 and then add 14 to get the sum of 54. Thus, (14+27) + 13 = 14 + (27 + 13). This property is known as the associativity of the addition of numbers. Express this property which we have already studied in the chapter on Whole Numbers, in a general way, by using variables a, b and c.
Answer: Let the three numbers be \( a \), \( b \), and \( c \). Then, the property called 'associativity of addition' can be shown as: \( a + (b + c) = (a + b) + c \).
In simple words: This rule means that when you add three numbers together, it doesn't matter which two you add first. You will always get the same total answer.

Exam Tip: The associative property is key for simplifying calculations and understanding number operations. It applies to addition and multiplication, but not subtraction or division.