>> Elementary Mathematics >> Triangle

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1). In, two similar triangles \( \Large \triangle \) ABC and \( \Large \triangle \) DEF, DE = 3 cm, EF = 5 cm, DF = 4 cm and BC = 20 cm, then length of AB is equal to
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2). If angles of one triangle are respectively equal to the angles of another triangle, then ratio of the corresponding sides is ratio of the corresponding
Correct Answer: all of these
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3). The locus of the vertex A of an isosceles triangle, ABC which has BC as its fixed base is
Correct Answer: perpendicular bisector of BC
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4). If AB and CD are two chords intersecting at a point P inside the circle such that AP = CP, then consider the following statements : Assertion (A) : AB = CD, Reason (R) : APC and DPB are similar triangles Of these statements
Correct Answer: both A and R are true, and R is correct explanation of A.
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5). If a triangle and a rectangle have equal areas and equal altitude, then base of the triangle is equal to
Let h be the common height of triangle and the rectangle. If a and b respectively be the bases of triangle and rectangle, then by hypothesis \( \Large \frac{1}{2}a \times h = b \times h \) => \( \Large \frac{1}{2}a = b \) => a = 2b | ||||

6). Area of an isosceles right-angled triangle is 800 sq. metres. The greatest possible square has been cut out from it. The length of the diagonal of this square will be
Let x be the base and side of isosceles \( \Large \triangle ABC \). Therefore, Length of diagonal of the square = \( \Large 20 \sqrt{2} m \) | ||||

7). If perimeter of a triangle is 100 m and its sides are in the ratio 1 : 2 : 2, then area of the triangle (in \( \Large m^{2} \)) is
Let the Sides. be x, 2x and 2x. | ||||

8). In the given figure, AD is the internal bisector and AE is the external bisector of \( \Large \angle \)BAC of any \( \Large \triangle \) ABC. Then which one of the following statements is not correct?
Correct Answer: \( \Large AC^{2} = DC \times CE \)
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9). In the given figure, \( \Large \angle \)ABC = \( \Large \angle \)ADB = \( 90^{\circ} \), which one of the following statements does not hold good?
(a) \( \Large \triangle ABC - \triangle ADB - \triangle CDB \) | ||||

10). Area of an equilateral triangle of side x is
\( \Large AD = \sqrt{AB^{2}-BD^{2}} \) = \( \Large \sqrt{x^{2}-\frac{x^{2}}{4}} \) = \( \Large \frac{\sqrt{3}}{2}x \) Therefore, Area of \( \Large \triangle ABC = \frac{1}{2} \times BC \times AD \) = \( \Large \frac{1}{2} \times x \times \frac{x\sqrt{3}}{2} \) = \( \Large \frac{\sqrt{3}}{4}x^{2} \) |