CASE STUDY QUESTION 9-Class X-Maths
Points A and B are on the opposite edges of a pond as shown in below figure. To find the distance between the two points, Ram makes a right-angled triangle using rope connecting B with another point C at a distance of 12 m, connecting C to point D at a distance of 40 m from point C and then connecting D to the point A which is at a distance of 30 m from D such that ∠ADC = 900
(a) Which property of geometry will be used to find the distance AC?
(i) Similarity of Triangles (ii) Thales Theorem
(iii) Pythagoras Theorem (iv) Quadratic Equation
Ans: (iii) Pythagoras Theorem
(b) What is the distance AC?
(i) 50 m (ii) 12 m (iii) 100 m (iv) 70 m
ADC is a right-angled triangle. By Pythagoras theorem we get
AC2=(30)2 + (40)2
⇒ AC2 = 900 + 1600
⇒ AC2 = 2500
⇒AC = 50m
(c) Which is the following does not form a Pythagoras triplet?
(i) (7, 24, 25) (ii) (15, 8, 17) (iii) (5, 12, 13) (iv) (21, 20, 28)
Ans: (iv) (21, 20, 28)
(d) Find the length AB.
(i) 12 m (ii) 38 m (iii) 50 m (iv) none of these
AC = 50m and BC = 12m
⇒ AB = AC – BC
⇒ AB = 50 – 12 = 38m
(e) Find the length of the rope used.
(i) 120 m (ii) 70 m (iii) 82 m (iv) none of these
Ans: (iii) Length of the rope used = 30 + 40 + 12 = 82 m