**Exercise 11.1**

*Question 1*

*Let the side of an equilateral triangle be m. Show the perimeter of the triangle with the help of m.*

**Answer**

Perimeter = sum of three sides

= m+m+m

= 3m

*Question 2*

*Let the side of a regular hexagon be denoted by m. Show the perimeter of the hexagon with the help of m.*

*(All sides are equal in regular hexagon)*

**Answer**

Side of regular hexagon = m

Perimeter = sum of all sides

= 6m

*Question 3*

*In the given figure a cube, 3 – D cube is shown. It has six identical squares as all the sides are equal so same six faces. Let the length of a side of cube be given by m. Find formula for total length of the cube.*

**Answer**

Length of an edge = m

Number of edges = 12

Total length of the edges = total number of edges × Length of each edge

= 12m

*Question 4*

*Diameter of a circle is a line which passes through the centre and joins two points of circle. (In the given figure XY is a diameter of circle; c is centre.) Express the diameter of the circle (d) in form of its radius(r).*

**Answer**

d = twice the radius

= 2r

**Exercise 11.2**

*Question 1*

*Make as many expressions with no. as you can from three numbers 2, 6 and 9. Each no. should be used only once. Use only addition, multiplication and subtraction.*

**Answer**

We can make many expressions using 2, 6 and 9 as given below.

9+ (6 – 2)

9 + (6 × 2)

(6 – 2) + 9

(6 + 2) × 9

(2 + 9) – 6

(2 × 9) × 6

*Question 2*

*Which of these expressions are formed with numbers only?*

- y + 6
- (8 × 10) – 6p
- 9 (15 – 7) + 6 × 4
- 9n
- 11
- 7 – 7m
- (2 × 40) – (4 × 20) – 25 + q

**Answer**

From above expressions given, it can be observed that option (c) and (e) are formed by using numbers only.

*Question 3 *

*Identify the operations and tell how the expressions have been formed.*

- a + 2, a – 2, b + 13, b – 13
- 7t, t/7, 15t
- 4x + 13, 4x – 13
- 8c, -8c + 2, -8m – 2

**Answer**

1. Addition: 2 is added to a

Subtraction: 2 is subtracted from a

Addition: 13 is added to b

Subtraction: 13 is subtracted from b

2. Multiplication: t is multiplied with 7

Division: t is divided by 7

Multiplication: t is multiplied with 15

3.Multiplication and addition: 4 is multiplied with x and result is added to 13.

Multiplication and subtraction: 4 is multiplied with x and 13 is subtracted from the result.

4. Multiplication: 8 is multiplied with c

Multiplication and addition: -8 is multiplied by c and add 2 to the result.

Multiplication and subtraction: c is multiplied with -8 and 2 is subtracted from the result.

*Question 4*

*Give expressions for the below:*

- 3 added to m
- 3 subtracted from m
- m multiplied by 8
- n divided by 8
- 9 subtracted from –n
- –m multiplied by 6
- –n divided by 6
- n multiplied by -9

**Answer**

- m + 3
- m – 3
- 8m
- n/8
- –n – 9
- -6m
- –n/6
- -9n

*Question 5*

*Give expressions for the following cases*

- 15 added to 3p
- 15 subtracted from 3p
- 7 times x to which 6 is added
- 7 times x from which 6 is subtracted
- z is multiplied by -9
- z is multiplied by -5 and then 3 is added to the result
- q is multiplied by 8 and the result is subtracted from 12
- q is multiplied by -8 and the result is added to 12

**Answer**

- 3p + 15
- 3p – 15
- 7x + 6
- 7x – 6
- -9z
- -5z + 3
- 12 – 8q
- -8q + 12

*Question 6*

*(a) Form expressions with s and 5. Use only one operation in the expressions. Every expression should have s in it.*

*(b) Form expressions with t, 3 and 8. Every expression should have t. Use only two operations. These two operations should be different.*

**Answer**

(a) s + 5

s – 5

5s

\(\frac{s}{5}\) \(\frac{5}{s}\)5 – s

(b) 3t + 8

3t – 8

8t + 3

8t – 3 etc..