Question

Match the following columns:

Column I	Column II
(a) A man goes 10 m due east and then 20 m due north. His distance from the starting point is ...... m.	(p) `25sqrt(3)`
(b) In an equilateral triangle with each side 10 cm, the altitude is ...... cm.	(q) `5sqrt(3)`
(c) The area of an equilateral triangle having each side 10 cm is ...... cm2.	(r) `10sqrt(5)`
(d) The length of diagonal of a  rectangle having length 8 m and  breadth 6 m is ...... m.	(s) 10

Answer 1

Column I	Column II
(a) A man goes 10 m due east and then 20 m due north. His distance from the starting point is ...... m.	(r) `10sqrt(5)`
(b) In an equilateral triangle with each side 10 cm, the altitude is ...... cm.	(q) `5sqrt(3)`
(c) The area of an equilateral triangle having each side 10 cm is ...... cm2.	(p) `25sqrt(3)`
(d) The length of diagonal of a  rectangle having length 8 m and  breadth 6 m is ...... m.	(s) 10

Explanation:

(a) Let OA = 10 m and AB = 20 m.

Then, OB² = OA² + AB²

= {(10)² + (20)²} m² 

= 500 m²

⇒ `OB = sqrt(500)  m`

= `sqrt(5 xx 100)  m`

= `10sqrt(5)  m`

(b) Altitude = `sqrt(3)/2 a`

= `(sqrt(3)/2 xx 10) cm`

= `5sqrt(3)  cm`

(c) Area = `sqrt(3)/4 a^2`

= `(sqrt(3)/4 xx 10 xx 10) cm^2`

= `25sqrt(3)  cm^2`

(d) d² = (8² + 6²) m²

= (64 + 36) m²

= 100 m²

⇒ `d = sqrt(100)  m`

= 10 m