S Chand ICSE Mathematics Class 9 Solution Tenth Chapter Pythagoras Theorem Exercise 10A (O.P. Malhotra, S.K. Gupta, Anubhuti Gangal)

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, AB2 = BC2 + AC2 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 = 90o. 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:


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