Term 1 Maths - VAGA Study

Chap 4

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CHAPTER 4

TRIANGLES

1. In the given figure, DE z BC . The value of EC is

length 2p . If AD = BC then the value of AD is (a) 3 (b) 3 p (c) 2p (d) 4p

Sol : cbse.site/ma/fm103

(a) 1.5 cm (b) 3 cm (c) 2 cm (d) 1 cm Sol : cbse.site/ma/fm101

2. In the given figure, x is

4. Which of the following statement is false? (a) All isosceles triangles are similar. (b) All quadrilateral are similar. (c) All circles are similar. (d) None of the above

Sol : cbse.site/ma/fm104

5. Two poles of height 6 m and 11 m stand vertically upright on a plane ground. If the distance between their foot is 12 m, then distance between their tops is (a) 12 m (b) 14 m (c) 13 m (d) 11 m

Sol : cbse.site/ma/fm105

Sol :

(a) (b)

ab aa+c b b+c

(c) (d)

bc b a+cc a+c

Sol : cbse.site/ma/fm102

3. TABC is an equilateral triangle with each side of

6. In a right angled TABC right angled at B , if P and

Q are points on the sides AB and BC respectively,

then (a) AQ2 + CP2 = 2^AC2 + PQ2h (b) 2^AQ2 + CP2h = AC2 + PQ2 (c) AQ2 + CP2 = AC2 + PQ2

(d)

AQ + CP =

1 2

^AC

+

PQh

Sol : cbse.site/ma/fm106

7. It is given that, TABC + TEDF such that AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm then the sum of the remaining sides of

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Triangles

Chap 4

the triangles is (a) 23.05 cm (b) 16.8 cm (c) 6.25 cm (d) 24 cm

Sol : cbse.site/ma/fm107

8. The area of a right angled triangle is 40 sq cm and its perimeter is 40 cm. The length of its hypotenuse is (a) 16 cm (b) 18 cm (c) 17 cm (d) data insufficient

Sol : cbse.site/ma/fm108

9. The areas of two similar triangles ABC and PQR are in the ratio 9 : 16. If BC = 4.5 cm, then the length of QR is (a) 4 cm (b) 4.5 cm (c) 3 cm (d) 6 cm

Sol : cbse.site/ma/fm109

10. If ratio of corresponding sides of two similar triangles is 5 : 6, then what is the ratio of their areas? (a) 6 : 5 (b) 5 : 6 (c) 25 : 36 (d) 36 : 25

Sol : cbse.site/ma/fm110

11. In the given figure, P and Q are points on the sides AB and AC respectively of a triangle ABC . PQ is parallel to BC and divides the triangle ABC into 2 parts, equal in area. The ratio of PA : AB =

(b) ( 2 - 1) : 2 (c) 1 : 2 (d) ( 2 - 1) : 1

Sol : cbse.site/ma/fm111

12.

It is given that TABC + TPQR

Then

ar (TPRQ) ar (TBCA)

is

equal

to

with

BC QR

=

1 4

.

(a) 16

(b) 3

(c)

1 4

(d)

1 16

Sol : cbse.site/ma/fm112

13. IfTABC + TAPQ and ar (TAPQ) = 4ar (TABC ), ar (TABC ), then the ratio of BC to PQ is (a) 2 : 1 (b) 1 : 2 (c) 1 : 4 (d) 4 : 1

Sol : cbse.site/ma/fm113

14. The areas of two similar triangles are 81 cm2 and 49 cm2 respectively, then the ratio of their corresponding medians is (a) 7 : 9 (b) 9 : 81 (c) 9 : 7 (d) 81 : 7

Sol : cbse.site/ma/fm114

15. Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio. (a) 2 : 3 (b) 4 : 9 (c) 81 : 16 (d) 16 : 81

Sol : cbse.site/ma/fm115

(a) 1 : 1

16. Assertion : In the 3ABC , AB = 24 cm, BC = 10 cm and AC = 26 cm, then 3ABC is a right angle

Chap 4

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triangle. Reason : If in two triangles, their corresponding angles are equal, then the triangles are similar. (a) Both assertion (A) and reason (R) are true and

reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true.

Sol : cbse.site/ma/fm116

17. Assertion : ABC and DEF are two similar triangles such that BC = 4 cm, EF = 5 cm and area of TABC = 64 cm2, then area of TDEF = 100 cm2. Reason : The areas of two similar triangles are in the ratio of the squares of the corresponding altitudes. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertion (A) is true but reason (R) is false.

Sol : cbse.site/ma/fm117

length of one of its altitude is ................... . (a) a 3 (b) a2 3 (c) a3 2 (d) a 2

Sol : cbse.site/ma/fm119

20. TABC and TBDE are two equilateral triangle such that D is the mid-point of BC . Ratio of the areas of triangles ABC and BDE is ................. . (a) 1 : 1 (b) 3 : 1 (c) 2 : 1 (d) 4 : 1

Sol : cbse.site/ma/fm120

21. A ladder 10 m long reaches a window 8 m above the ground. The distance of the foot of the ladder from the base of the wall is ................ m. (a) 8 m (b) 2 m (c) 6 m (d) 4 m

Sol : cbse.site/ma/fm121

18. Assertion : 3ABC + 3DEF such that ar (3ABC) = 36 cm2 and ar^3DEF h = 49 cm2 then, AB : DE = 6 : 7.

Reason : If 3ABC + 3DEF , then

ar^3ABC h ar ^3DEF h

=

AB2 DE2

=

BC2 EF2

=

AC2 DF2

(a) Both assertion (A) and reason (R) are true and

reason (R) is the correct explanation of assertion

(A).

(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

(c) Assertion (A) is true but reason (R) is false.

(d) Assertion (A) is false but reason (R) is true.

Sol : cbse.site/ma/fm118

19. TABC is an equilateral triangle of side 2a , then

22. In TABC , AB = 6 3 cm, AC = 12 cm and BC = 6 cm, then +B = .................. . (a) 30c (b) 60c (c) 45c (d) 90c

Sol : cbse.site/ma/fm122

23. The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of the first triangle is 9 cm, then the corresponding side of second triangle is ................... . (a) 4.2 cm (b) 5.4 cm (c) 20 cm (d) 6 cm

Sol : cbse.site/ma/fm123

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Chap 4

24. If TABC + TPQR , and

ar (TABC) (aar)(T13 PQR)

=

?

(b)

1 9

(c)

8 9

(d)

5 9

Sol : cbse.site/ma/fm124

AB PQ

=

1 3

,

then

25. In figure, MN < BC and AM : MB = 1 : 2, then

ar (TAMN) ar (TABC)

=

...................

.

be

(a)

1 3

(b)

1 9

(c)

8 9

(d)

5 9

Sol : cbse.site/ma/fm128

29. In TABC, DE | | BC, the value of x will be

(a)

1 3

(b)

1 9

(c)

8 9

(d)

5 9

Sol : cbse.site/ma/fm125

26. The corresponding sides of two similar triangles

are in the ratio 3 : 4, then the ratio of the areas of

triangles is ...................

(a)

1 3

(b)

1 9

(c)

9 16

(d)

3 4

Sol : cbse.site/ma/fm126

27. The perimeters of two similar triangles TABC and

TPQR are 35 cm and 45 cm respectively, then the

ratio of the areas of the two triangles is .........

(a)

2 9

(b)

7 9

(c)

49 81

(d)

3 4

Sol : cbse.site/ma/fm127

(a) 1 (b) 2 (c) 3 (d) 4

Sol : cbse.site/ma/fm129

30. TABC is isosceles with AC = BC . If AB2 = 2AC2, then the measure of +C will be (a) 30c (b) 60c (c) 45c (d) 90c Sol : cbse.site/ma/fm130

31. In Figure, DE | | BC and given that AE = 1.8 cm, BD = 7.2 cm and CE = 5.4 cm. The length of side AD will be

28.

If TABC + TPQR ,

AB PQ

=

1 3

,

then

arTABC arTPQR

will

(a) 1.6 cm

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(b) 1.9 cm (c) 2.1 cm (d) 2.4 cm

Sol : cbse.site/ma/fm131

34. In given figure DE | | BC. If AD = 3c, DB = 4c cm and AE = 6 cm then EC will be

32. In the given figure, if +A = 90?,+B = 90?, OB = 4.5 cm OA = 6 cm and AP = 4 cm then QB will be

(a) 12 cm (b) 6 cm (c) 8 cm (d) 10 cm

Sol : cbse.site/ma/fm134

(a) 2 cm (b) 3 cm (c) 4 cm (d) 6 cm

Sol : cbse.site/ma/fm132

33.

In the KN =

figure, PQ is parallel to MN. 20.4 cm then KQ will be

If

KP PM

=

4 13

and

35. If triangle ABC is similar to triangle DEF such that 2AB = DE and BC = 8 cm then EF will be (a) 16 cm (b) 14 cm (c) 12 cm (d) 10 cm

Sol : cbse.site/ma/fm135

36.

In

Figure

+D = +E

and

AD DB

=

AE EC

,

then TBAC

is

(a) 4.1 cm (b) 5.2 cm (c) 4.8 cm (d) 5.4 cm

Sol : cbse.site/ma/fm133

(a) isosceles triangle (b) scalene triangle (c) equilateral triangle (d) right angle triangle Sol : cbse.site/ma/fm136

37. In Figure, ABC is an isosceles triangle right angled

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