Practice Set 2.1 | Q 1.1 | Page 38
Identify, with reason, if the following is a Pythagorean triplet.
(3,5,4)
Practice Set 2.1 | Q 1.2 | Page 38
Identify, with reason, if the following is a Pythagorean triplet.
(4, 9, 12)
Practice Set 2.1 | Q 1.3 | Page 38
Identify, with reason, if the following is a Pythagorean triplet. (5, 12, 13)
Practice Set 2.1 | Q 1.4 | Page 38
Identify, with reason, if the following is a Pythagorean triplet.
(24, 70, 74)
Practice Set 2.1 | Q 1.5 | Page 38
Identify, with reason, if the following is a Pythagorean triplet.
(10, 24, 27)
Practice Set 2.1 | Q 1.6 | Page 38
Identify, with reason, if the following is a Pythagorean triplet.
(11, 60, 61)
Practice Set 2.1 | Q 2 | Page 38
In the given figure, ∠MNP = 90°, seg NQ ⊥seg MP, MQ = 9, QP = 4, find NQ.
Practice Set 2.1 | Q 3 | Page 38
In the given figure, ∠QPR = 90°, seg PM ⊥ seg QR and Q–M–R, PM = 10, QM = 8, find QR
Practice Set 2.1 | Q 4 | Page 39
In the given figure. Find RP and PS using the information given in ∆PSR.
Practice Set 2.1 | Q 5 | Page 39
For finding AB and BC with the help of information given in the figure, complete following activity.
AB = BC ……….
\[\therefore \angle BAC = \]
\[ \therefore AB = BC =\] \[\times AC\]
\[ =\] \[\times \sqrt{8}\]
\[ =\] \[\times 2\sqrt{2}\]
=
Practice Set 2.1 | Q 6 | Page 39
Find the side and perimeter of a square whose diagonal is 10 cm ?
.
Practice Set 2.1 | Q 7 | Page 39
In the given figure, ∠DFE = 90°, FG ⊥ ED, If GD = 8, FG = 12, find (1) EG (2) FD and (3) EF
Practice Set 2.1 | Q 8 | Page 39
Find the diagonal of a rectangle whose length is 35 cm and breadth is 12 cm.
Practice Set 2.1 | Q 9 | Page 39
In the given figure, M is the midpoint of QR. ∠PRQ = 90°. Prove that, PQ2 = 4PM2 – 3PR2
Practice Set 2.1 | Q 10 | Page 39
Walls of two buildings on either side of a street are parellel to each other. A ladder 5.8 m long is placed on the street such that its top just reaches the window of a building at the height of 4 m. On turning the ladder over to the other side of the street , its top touches the window of the other building at a height 4.2 m. Find the width of the street.
Practice Set 2.2 | Q 1 | Page 43
In ∆PQR, point S is the midpoint of side QR. If PQ = 11, PR = 17, PS = 13, find QR.
Practice Set 2.2 | Q 2 | Page 43
In ∆ABC, AB = 10, AC = 7, BC = 9 then find the length of the median drawn from point C to side AB
Practice Set 2.2 | Q 3 | Page 43
In the given figure, seg PS is the median of ∆PQR and PT ⊥ QR. Prove that,
(i) PR2 = PS2 + QR × ST + `(“QR”/2)^2`
(ii) PQ2 = PS2 – QR × ST + `(“QR”/2)^2`
Practice Set 2.2 | Q 4 | Page 43
In ∆ABC, point M is the midpoint of side BC.
If, AB2 + AC2 = 290 cm2, AM = 8 cm, find BC.
Practice Set 2.2 | Q 5 | Page 43
In the given figure, point T is in the interior of rectangle PQRS, Prove that, TS2 + TQ2 = TP2 + TR2 (As shown in the figure, draw seg AB || side SR and A-T-B)
Problem Set 2 | Q 1.1 | Page 43
Some question and their alternative answer are given. Select the correct alternative.
Out of the following which is the Pythagorean triplet?
(1, 5, 10)
(3, 4, 5)
(2, 2, 2)
(5, 5, 2)
Problem Set 2 | Q 1.2 | Page 43
Some question and their alternative answer are given.
In a right-angled triangle, if sum of the squares of the sides making right angle is 169 then what is the length of the hypotenuse?
15
13
5
12
Problem Set 2 | Q 1.3 | Page 43
Some question and their alternative answer are given. Select the correct alternative.
Out of the dates given below which date constitutes a Pythagorean triplet ?
15/08/17
16/08/16
3/5/17
4/9/15
Problem Set 2 | Q 1.4 | Page 43
Some question and their alternative answer are given. Select the correct alternative.
If a, b, c are sides of a triangle and a2 + b2 = c2, name the type of triangle.
Obtuse angled triangle
Acute angled triangle
Right angled triangle
Equilateral triangle
Problem Set 2 | Q 1.5 | Page 43
Some question and their alternative answer are given. Select the correct alternative.
Find perimeter of a square if its diagonal is \[10\sqrt{2}\]
10 cm
\[40\sqrt{2}\]cm
20 cm
40 cm
Problem Set 2 | Q 1.6 | Page 43
Some question and their alternative answer are given. Select the correct alternative.
Altitude on the hypotenuse of a right angled triangle divides it in two parts of lengths 4 cm and 9 cm. Find the length of the altitude.
9 cm
4 cm
6 cm
\[2\sqrt{6}\] cm
Problem Set 2 | Q 1.7 | Page 43
Some question and their alternative answer are given. Select the correct alternative.
Height and base of a right angled triangle are 24 cm and 18 cm find the length of its hypotenuse
24 cm
30 cm
15 cm
18 cm
Problem Set 2 | Q 1.8 | Page 43
Some question and their alternative answer are given. Select the correct alternative.
In ∆ABC, AB = \[6\sqrt{3}\] cm, AC = 12 cm, BC = 6 cm. Find measure of ∠A.
30°
60°
90°
45°
Problem Set 2 | Q 2.1 | Page 44
Solve the following example.
Find the height of an equilateral triangle having side 2a..
Problem Set 2 | Q 2.2 | Page 44
Do sides 7 cm, 24 cm, 25 cm form a right angled triangle ? Give reason
Problem Set 2 | Q 2.3 | Page 44
Find the length a diagonal of a rectangle having sides 11 cm and 60 cm.
Problem Set 2 | Q 2.4 | Page 44
Find the length of the hypotenuse of a right angled triangle if remaining sides are 9 cm and 12 cm.
Problem Set 2 | Q 2.5 | Page 44
A side of an isosceles right angled triangle is x. Find its hypotenuse.
Problem Set 2 | Q 2.6 | Page 44
In ∆PQR, PQ = √8 , QR = √5 , PR = √3. Is ∆PQR a right-angled triangle? If yes, which angle is of 90°?
Problem Set 2 | Q 3 | Page 44
In ∆RST, ∠S = 90°, ∠T = 30°, RT = 12 cm then find RS and ST.
.
Problem Set 2 | Q 4 | Page 44
Find the diagonal of a rectangle whose length is 16 cm and area is 192 sq.cm ?
Problem Set 2 | Q 5 | Page 44
Find the length of the side and perimeter of an equilateral triangle whose height is \[\sqrt{3}\] cm
Problem Set 2 | Q 6 | Page 44
In ∆ABC seg AP is a median. If BC = 18, AB2 + AC2 = 260 Find AP
Problem Set 2 | Q 7 | Page 45
∆ABC is an equilateral triangle. Point P is on base BC such that PC = \[\frac{1}{3}\] BC, if AB = 6 cm find AP.
Problem Set 2 | Q 8 | Page 45
From the information given in the figure, prove that PM = PN = \[\sqrt{3}\] × a
Problem Set 2 | Q 9 | Page 45
Prove that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.
Problem Set 2 | Q 10 | Page 45
Pranali and Prasad started walking to the East and to the North respectively, from the same point and at the same speed. After 2 hours distance between them was \[15\sqrt{2}\]
km. Find their speed per hour.
Problem Set 2 | Q 11 | Page 45
In ∆ABC, ∠BAC = 90°, seg BL and seg CM are medians of ∆ABC. Then prove that:
4(BL2 + CM2) = 5 BC2
Problem Set 2 | Q 12 | Page 45
Sum of the squares of adjacent sides of a parallelogram is 130 sq.cm and length of one of its diagonals is 14 cm. Find the length of the other diagonal
Problem Set 2 | Q 13 | Page 45
In ∆ABC, seg AD ⊥ seg BC, DB = 3CD.
Prove that: 2AB2 = 2AC2 + BC2
Problem Set 2 | Q 14 | Page 44
In an isosceles triangle, length of the congruent sides is 13 cm and its base is 10 cm. Find the distance between the vertex opposite the base and the centroid.
Problem Set 2 | Q 15 | Page 46
In a trapezium ABCD, seg AB || seg DC seg BD ⊥ seg AD, seg AC ⊥ seg BC, If AD = 15, BC = 15 and AB = 25. Find A(▢ABCD)
Problem Set 2 | Q 16 | Page 44
In the given figure, ∆PQR is an equilateral triangle. Point S is on seg QR such thatn QS =n\[\frac{1}{3}\] QR
Prove that : 9 PS2 = 7 PQ2
Problem Set 2 | Q 17 | Page 44
Seg PM is a median of ∆PQR. If PQ = 40, PR = 42 and PM = 29, find QR
Problem Set 2 | Q 18 | Page 46
Seg AM is a median of ∆ABC. If AB = 22, AC = 34, BC = 24, find AM