Frank solutions for Class 9 Maths ICSE chapter 17 - Pythagoras Theorem [Latest edition]

Chapter 17: Pythagoras Theorem

Exercise 17.1
Exercise 17.1

Frank solutions for Class 9 Maths ICSE Chapter 17 Pythagoras Theorem Exercise 17.1

Exercise 17.1 | Q 1

Find the length of the perpendicular of a triangle whose base is 5cm and the hypotenuse is 13cm. Also, find its area.

Exercise 17.1 | Q 2

Find the length of the hypotenuse of a triangle whose other two sides are 24cm and 7cm.

Exercise 17.1 | Q 3

Calculate the area of a right-angled triangle whose hypotenuse is 65cm and one side is 16cm.

Exercise 17.1 | Q 4

A man goes 10 m due east and then 24 m due north. Find the distance from the straight point.

Exercise 17.1 | Q 5

A ladder 25m long reaches a window of a building 20m above the ground. Determine the distance of the foot of the ladder from the building.

Exercise 17.1 | Q 6

A right triangle has hypotenuse p cm and one side q cm. If p - q = 1, find the length of third side of the triangle.

Exercise 17.1 | Q 7

A ladder 15m long reaches a window which is 9m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to other side of the street to reach a window 12m high. Find the width of the street.

Exercise 17.1 | Q 8

The foot of a ladder is 6m away from a wall and its top reaches a window 8m above the ground. If the ladder is shifted in such a way that its foot is 8m away from the wall to what height does its tip reach?

Exercise 17.1 | Q 9

Two poles of height 9m and 14m stand on a plane ground. If the distance between their 12m, find the distance between their tops.

Exercise 17.1 | Q 10

The length of the diagonals of rhombus are 24cm and 10cm. Find each side of the rhombus.

Exercise 17.1 | Q 11

Each side of rhombus is 10cm. If one of its diagonals is 16cm, find the length of the other diagonals.

Exercise 17.1 | Q 12

In ΔABC, AD is perpendicular to BC. Prove that: AB2 + CD2 = AC2 + BD2

Exercise 17.1 | Q 13

In an equilateral triangle ABC, the side BC is trisected at D. Prove that 9 AD2 = 7 AB2.

Exercise 17.1 | Q 14.1

From a point O in the interior of aΔABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove that: AF2 + BD2 + CE= OA2 + OB2 + OC2 - OD2 - OE2 - OF2

Exercise 17.1 | Q 14.2

From a point O in the interior of aΔABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove that: AF2 + BD2 + CE2 = AE2 + CD2 + BF2

Exercise 17.1 | Q 15.1

In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC2 = AD2 + BC x DE + (1)/(4)"BC"^2

Exercise 17.1 | Q 15.2

In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB2 = AD2 - BC x CE + (1)/(4)"BC"^2

Exercise 17.1 | Q 15.3

In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB2 + AC2 = 2AD2 + (1)/(2)"BC"^2

Exercise 17.1 | Q 15.4

In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC2 - AB2 = 2BC x ED

Exercise 17.1 | Q 15.5

In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB2 + AC2 = 2(AD2 + CD2)

Exercise 17.1 | Q 16

A point OI in the interior of a rectangle ABCD is joined with each of the vertices A, B, C and D. Prove that  OB2 + OD2 = OC2 + OA2

Exercise 17.1 | Q 17

ABCD is a rhombus. Prove that AB2 + BC2 + CD2 + DA2= AC2 + BD2

Exercise 17.1 | Q 18

AD is perpendicular to the side BC of an equilateral ΔABC. Prove that 4AD2 = 3AB2.

Exercise 17.1 | Q 19

The perpendicular AD on the base BC of a ∆ABC intersects BC at D so that DB = 3 CD. Prove that 2"AB"^2 = 2"AC"^2 + "BC"^2

Exercise 17.1 | Q 20.1

In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.
Prove that: 9AQ2 = 9AC2 + 4BC2

Exercise 17.1 | Q 20.2

In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.
Prove that: 9BP2 = 9BC2 + 4AC2

Exercise 17.1 | Q 20.3

In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.
Prove that : 9(AQ2 + BP2) = 13AB2

Exercise 17.1 | Q 21

In the given figure, PQ = "RS"/(3) = 8cm, 3ST = 4QT = 48cm.
SHow that ∠RTP = 90°.

Exercise 17.1 | Q 22

In a right-angled triangle ABC,ABC = 90°, AC = 10 cm, BC = 6 cm and BC produced to D such CD = 9 cm. Find the length of AD.

Exercise 17.1 | Q 23

In the given figure. PQ = PS, P =R = 90°. RS = 20 cm and QR = 21 cm. Find the length of PQ correct to two decimal places.

Exercise 17.1 | Q 24

In a right-angled triangle PQR, right-angled at Q, S and T are points on PQ and QR respectively such as PT = SR = 13 cm, QT = 5 cm and PS = TR. Find the length of PQ and PS.

Exercise 17.1 | Q 25

PQR is an isosceles triangle with PQ = PR = 10 cm and QR = 12 cm. Find the length of the perpendicular from P to QR.

Exercise 17.1 | Q 26

In a square PQRS of side 5 cm, A, B, C and D are points on sides PQ, QR, RS and SP respectively such as PA = PD = RB = RC = 2 cm. Prove that ABCD is a rectangle. Also, find the area and perimeter of the rectangle.

Exercise 17.1

Frank solutions for Class 9 Maths ICSE chapter 17 - Pythagoras Theorem

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Concepts covered in Class 9 Maths ICSE chapter 17 Pythagoras Theorem are Regular Polygon, Right-angled Triangles and Pythagoras Property, Right-angled Triangles and Pythagoras Property.

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