Triangles - SSC

In triangle ABC, the bisector of angle BAC meets BC at point D in such a way that AB = 10  cm. AC = 15 cm and BD = 6 cm. Find the length of BC (in cm).

• A.

  17

• B.

  11

• C.

  15

• D.

  9

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In a ∆ABC, D, E and F are the mid-points of side BC, CA and AB respectively. If BC = 25.6 cm. CA = 18.8 cm and AB = 20.4 cm, what is the perimeter (in cm) of the ∆DEF?

• A.

  36.8

• B.

  30.6

• C.

  32.4

• D.

  34.4

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The area of quadrilateral is 336 and the perpendiculars drawn to one diagonal from the opposite vertices are 16 m and 12 m long. Find the length of this diagonal.

• A.

  28 cm

• B.

  26 cm

• C.

  21 cm

• D.

  24 cm

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Find the area of a triangle with sides 3 cm, 4 cm, and 5 cm.

• A.

  8.5 cm²

• B.

  7 cm²

• C.

  6 cm²

• D.

  10 cm²

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Two triangles ΔABC and ΔDEF are similar. If AB = 6 cm, BC = 8 cm and DE = 9 cm, find EF.

• A.

  12 cm

• B.

  9 cm

• C.

  10 cm

• D.

  8 cm

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The height and slant height of a conical vessel are 12 cm and 13 cm, respectively. The capacity of the vessel is: (Use π = 3.14)

• A.

  0.314 litres

• B.

  0.424 litres

• C.

  0.5 litres

• D.

  0.298 litres

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If ∆ABC ~ ∆QRP, $\frac{ar(∆ABC)}{ar(∆QRP)}$ = $\frac{9}{4}$, AB=18 cm, BC=15 cm, then the length of PR is ______.

• A.

  10 cm

• B.

  12 cm

• C.

  16 cm

• D.

  14 cm

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The height of a right circular cone is 6 cm and its base diameter is 16 cm. Find the volume of this cone.

• A.

  384π cm³

• B.

  786π cm³

• C.

  128π cm³

• D.

  512π cm³

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What will be the area of a triangle whose sides are 13 cm, 5 cm and 12 cm?

• A.

  40 cm²

• B.

  50 cm²

• C.

  30 cm²

• D.

  35 cm²

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For what angle D is ∆ABC congruent to ∆DEF, given AC = 2.5 cm, BC = 5 cm, ∠C = 75°, DE = 2.5 cm and DF = 5 cm?

• A.

  75°

• B.

  25°

• C.

  35°

• D.

  90°

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The area of a triangle is 96 cm² and the length of one of its sides is 24 cm. What is the length of the perpendicular drawn to this side of the triangle from the opposite vertex?

• A.

  16 cm

• B.

  8 cm

• C.

  4 cm

• D.

  12 cm

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 In a triangle ABC, if the three sides are a=5, b=7 and c=3, what is angle B?

• A.

  1200

• B.

  600

• C.

  900

• D.

  1500

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The ratio of measures of the angles of a triangle is given as 3 : 4 : 8. What is the measure of the smallest of the three angles?

• A.

  33°

• B.

  39°

• C.

  30°

• D.

  36°

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If AB = QR, BC = PR and CA = PQ, then

• A.

  △PQR ≅ △BCA

• B.

  △ABC ≅ △PQR

• C.

  △CBA ≅ △PRQ

• D.

  △BAC ≅ △RPQ

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If the circumradius of an equilateral triangle is 18 cm, then the measure of its in-radius is:

• A.

  9 cm

• B.

  3 cm

• C.

  10 cm

• D.

  12 cm

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 If triangles ABC and PQR are both isosceles with AB = AC and PQ = PR, respectively. If also AB = PQ and BC = QR and angle B = 50°, then what is the measure of angle R?

• A.

  50°

• B.

  80°

• C.

  90°

• D.

  60°

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In a triangle ∆ABC, right angle at B, if tan A = $\frac{1}{\sqrt{3}}$, then sin A. cos C + cos A. sin C = _______.

• A.

  0

• B.

  2

• C.

  -1

• D.

  1

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In a right triangle ABC, right angled at B, altitude BD is drawn to the hypotenuse AC of the triangle. If AD = 6 cm, CD = 5 cm. then find the value of AB² + BD² (in cm).

• A.

  30

• B.

  66

• C.

  36

• D.

  96

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Let △ABC − △QPR and (Area of △ABC) : (Area of △PQR) = 121 : 64. If QP = 14.4 cm, PR = 12 cm and AC = 18 cm, then what is the length of AB?

• A.

  19.8 cm

• B.

  32.4 cm

• C.

  21.6 cm

• D.

  16.2 cm

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In a △ABC, D, E and Fare the mid-points of side BC, CA and AB respectively. If BC = 14.4 cm, CA = 15.2 cm and AB= 12.4 cm, what is the perimeter (in cm) of the △DEF?

• A.

  35

• B.

  28

• C.

  42

• D.

  21

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In a △ABC, the bisector of ∠A meets BC at D. If AB = 9.6 cm. AC = 11.2 cm and BD = 4.8 cm, the perimeter (in cm) of △ABC is:

• A.

  30.4

• B.

  28.6

• C.

  31.2

• D.

  32.8

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In △ABC , D is a point on side BC such that ∠ADC = ∠BAC. If CA = 12 cm and CD = 8 cm, then CB (in cm) =?

• A.

  18

• B.

  10

• C.

  12

• D.

  15

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In a triangle ABC, D and E are points on BC such that AD = AE and ∠BAD - ∠CAE. If AB = (2p + 3), BD = 2p. AC = (3q - 1) and CE = q, then find the value of (p + q).

• A.

  3

• B.

  3.6

• C.

  4.5

• D.

  2

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The difference between the two perpendicular sides of a right-angled triangle is 17 cm and its area is 84 cm². What is the perimeter (in cm) of the triangle?

• A.

  40

• B.

  49

• C.

  36

• D.

  56

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The lengths of the three sides of a right-angled triangle are (x - 1) cm, (x - 1) cm and (x + 3} cm, respectively. The hypotenuse of the right-angled triangle (in cm) is:

• A.

  6

• B.

  10

• C.

  12

• D.

  7

• View Answer