**S Chand ICSE Mathematics Class 9 Solution Tenth Chapter Pythagoras Theorem Exercise 10A**

**(1) In a right angled triangle ABC, c is the length of the hypotenuse, and a and b are other two sides.**

**(i) If a = 6 and b = 8, then find c.**

**(ii) If c = 25 and a = 24, then find b.**

**(iii) If c = 13 and b = 5, them find a.**

**(iv) If a = 10 and c = 21, then find b.**

**(v) if a = 9 and b = 9, then find c.**

**(2) A rectangular field is 30 m by 40 m. What distance is saved by walking diagonally across the field?**

**(3) A man travels 7 km due north, then goes 3 km due east and then 3 km due south. how far is he form his starting point?**

**(4) The diagonals of a rhombus are 12 cm and 9 cm long. Calculate the length of one side of the rhombus.**

**(5) (i) In a right-angled triangle ABC it is given that the hypotenuse, AC = 2.5 cm, and the side AB = 1.5 cm. Calculate the side BC.**

**(ii) AD is drawn perpendicular to BC, base of an equilateral triangle ABC. Given BC = 10 cm, find the length of AD, correct to one decimal place of decimal.**

**(6) ABC is right angled triangle. Angle ABC = 90 degree, AC = 25 cm and AB = 24 cm. Calculate the area of ΔABC.**

**(7) A ladder 13 m long tests against a vertical wall, If the foot of the ladder is 5 m from the foot of the wall, find the distance of the other end of the ladder from ground.**

**(8) Use the given information to make a neat diagram of the figure having given properties and write down the name of the figures.**

**In triangle ABC, AB ^{2} = BC^{2} + AC^{2} and AC = 2BC.**

**(9) In fig 10.10, ABCD represents a quadrilateral in which AD = 13 cm, DC = 12 cm, BC = 3 cm, and ****∠****ABD = ****∠****BCD = 90 ^{o}. Calculate the length of AB.**

**(10) Which of the triangles whose sides are given are given below are right angled?**

**(i) 4 cm, 5 cm, 6 cm**

**(ii) 1.2 cm, 3.7 cm, 3.5 cm.**

**(iii) 4 cm, 9.6 cm, 10.4 cm**

**(iv) 2.2 cm, 3.3 cm, 4.4 cm.**

**(11) In Fig. 10.11, find the distance of D from A, unit of length is cm, (AB = 2, BC = 4, CD = 2)**

**(12) The sides of a right angled triangle containing the right angle are 5x and (3x – 1) cm. If the area of the triangle be 60 cm square, calculate the lengths of the sides of the triangle.**

**Solution: **

**(13) In Fig. 10.12 its is given that AB = BC = 25 cm, AE = 7 m, and CD = 24 m, find the length of DE and also show that triangle ABE and triangle BDC are congruent.**

**(14) A ladder rests against a vertical wall at a height of 12 m from the ground with its foot at a distance of 9 m from the wall on the ground. If the foot of the ladder is shifted 3 m away from the wall, how much lower will the ladder slide down?**

**Solution: **

**(15) AD is an altitude of a ****△****ABC and AD is 12 cm BD = 9 cm and DC = 16 cm long respectively. Prove that the angle BAC is a right angle.**

**Solution: **

**(16) The shortest distance AP from a point A to a straight line QR is 12 cm, and Q , R are 15 cm and 20 cm distance from A on opposite sides of AP, prove that QAR is a right angle.**

**(17) In Fig. 10.13, PT is an altitude of the triangle PQR, In which PQ – 25 cm, PR = 17 cm, PT = 15 cm and QR = x cm. Calculate x.**

**(18) In Fig. 10.14, AB = 8 cm, BC = 6 cm, AC = 3 cm and the angle ADC = 90 degree, calculate CD.**

**Solution: **

**(19) In Fig. 10.15, the angle BAC is a right angle and AD is perpendicular to BC; AB = 4 cm and AC = 3 cm and BD = x, Calculate x**

**Solution: **

**(20) In fig. 10.16, the angle BAD and ADC are right angles and AX is parallel to BC. If AB = BC = 5 cm, and DC = 8 cm, Calculate the area of ABCX.**

**Solution: **