>> Elementary Mathematics >> Triangle
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
A). 15 cm
B). 12 cm
C). 10 cm
D). 6 cm
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
A). medians
B). bisector angles (angle bisector segments)
C). altitude
D). all of these
3). The locus of the vertex A of an isosceles triangle, ABC which has BC as its fixed base is
A). a line parallel to BC
B). a line perpendicular to BC
C). a circle with BC as a diameter
D). perpendicular bisector of BC
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

A). both A and R are true, and R is correct explanation of A.
B). both A and R are true, but R is not a correct explanation of A.
C). A is true, but R is false.
D). A is false, but R is true
5). If a triangle and a rectangle have equal areas and equal altitude, then base of the triangle is equal to
A). base of the rectangle.
B). twice the base of the rectangle.
C). thrice the base of the rectangle.
D). four times the base of the rectangle

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
A). \( \Large 10\ \sqrt{2} m\)
B). \( \Large 10\ \sqrt{3} m\)
C). 20 m
D). \( \Large 20\ \sqrt{2} m\)
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
A). \( \Large 100 \sqrt{3} \)
B). \( \Large 100 \sqrt{15} \)
C). \( \Large 100 \sqrt{5} \)
D). \( \Large 100 \sqrt{7} \)
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?
A). \( \Large AC^{2} = DC \times CE \)
B). \( \Large AC \times CD = AC \times BD \)
C). \( \Large AB : AC = BE : CE \)
D). \( \Large \angle ADE - 90 ^{\circ} \)
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, ADB and CDB are similar.
B). \( \Large AD \times DC \)
C). \( \Large \triangle ADB : \triangle CDB = AB : BC \)
D). \( \Large AB^{2} = AD \times AC \)
10). Area of an equilateral triangle of side x is
A). \( \Large \frac{x^{2}}{\sqrt{2}} \)
B). \( \Large \frac{\sqrt{3}}{4} x^{2} \)
C). \( \Large \frac{\sqrt{3}}{2} x^{2} \)
D). \( \Large \frac{\sqrt{3}}{2} x^{3} \)
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