Question

Vishnu’s mathematics teacher gave him four broom sticks, two broom sticks each of length 6cm and other two broom sticks each of length 8cm. Based on this information answer the following. (a) Which of the following quadrilateral can be made with the given broom sticks (without breaking)? (i) Rectangle (ii) Square (iii) Rhombus (iv) None (b) If Vishnu forms a quadrilateral with these brooms, what is the perimeter of the quadrilateral so formed? (i) 20 cm (ii) 24 cm (iii) 28 cm (iv) 30 cm (c) If Vishnu forms a Rectangle with these brooms, find the length of a diagonal. (i) 10 cm (ii) 12 cm (iii) 16 cm (iv) 18 cm (d) Which of the following properties of Rectangle is true? (i) Diagonals of rectangle are perpendicular. (ii) Diagonals of rectangle are equal. (iii) All sides of Rectangle all equal. (iv) Diagonals of Rectangle do not bisect each other. (e) If Vishnu forms a square by breaking only two broom sticks, what is the length of the diagonal of the square formed? (i) 6 cm (ii) 2√6 cm (iii) 12 cm (iv) 3√6 cm​

Answer 1

Answer:

@rectangle

b 28

c 10

d diagonals of rectangle do not bisect each other

Answer 2

Answer:

As given  below

step by step explanation:

Given data

the length of the broom sticks  set 1  = 6m

                                                    set 2 = 8 cm

Given questions

(a)  Which of the following quadrilateral can be made with the given broom sticks (without breaking)?

(i) Rectangle   (ii) Square   (iii) Rhombus   (iv) None  

ans:- (i) Rectangle

∵ The lengths of sticks are different and 2 sticks are with same length

b) If Vishnu forms a quadrilateral with these brooms, what is the perimeter of the quadrilateral so formed?

(i) 20 cm     (ii) 24 cm      (iii) 28 cm       (iv) 30 cm  

ans:- (iii) 28 cm

if Vishnu formed a quadrilateral it will be a rectangle

then dimension of quadrilateral  =  8 cm × 6 cm  

perimeter of quadrilateral = 2(8+6)  = 2(14) = 28 cm

(c) If Vishnu forms a Rectangle with these brooms, find the length of a diagonal.

(i) 10 cm     (ii) 12 cm      (iii) 16 cm    (iv) 18 cm  

ans:- (i) 10 cm    

      the diagonal of the rectangle  d = $\sqrt{a^{2} + b^{2} }$  

                           [ where a and b are sides of rectangle ]  

                           ⇒   d = √(6² + 8²)

                                  d = √100 = 10 cm

(d) Which of the following properties of Rectangle is true?

i) Diagonals of rectangle are perpendicular.

ii) Diagonals of rectangle are equal.

iii) All sides of Rectangle all equal.

iv) Diagonals of Rectangle do not bisect each other

ans:- ii) Diagonals of rectangle are equal.

[ ∵ Diagonals of a rectangles are equal ]

(e) If Vishnu forms a square by breaking only two broom sticks, what is the length of the diagonal of the square formed?

i) 6 cm      (ii) 2√6 cm      (iii) 12 cm     (iv) 3√6 cm​  

if Vishnu formed a square by breaking only two sticks then broken sticks will largest sticks which are 8 cm length  

and the length of the side of the square will be 6 cm  

        here diagonal of the square d = √2 (6)

                                                             = 6 √2 cm