CASE STUDY QUESTION 9-Class X-Maths

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

Ans: (i)

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

Ans: (ii)

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