# 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 = 90 ^{0}**

**(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

AC^{2}=(30)^{2} + (40)^{2}

⇒ AC^{2} = 900 + 1600

⇒ AC^{2} = 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

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