TRIANGLES Test

TRIANGLES

This is TRIANGLES Test-05 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
If PQR is an isosceles triangle and M is a point on QR such that \(PM \bot QR,\)then
  • A
    \(P{Q^2} + P{M^2} = QM.MR.\)
  • B
    \({\text{P}}{{\text{Q}}^2} - {\text{P}}{{\text{R}}^2}{\text{ = Q}}{{\text{M}}^2}{\text{ }} - {\text{ M}}{{\text{R}}^2}\)
    Correct
  • C
    \(P{Q^2} - P{M^2} = Q{M^2} - M{R^2}.\)
  • D
    \(P{Q^2} - P{M^2} = QM.MR.\)
2
Two poles of height 8 m and 13 m are standing 12 m apart. The distance between their tops is
  • A
    13 m.
    Correct
  • B
    15 m.
  • C
    17 m.
  • D
    19 m.
3
The length of the second diagonal of a rhombus whose side is 5 cm and one of the diagonal is 8 cm is
  • A
    6 cm.
    Correct
  • B
    14 cm
  • C
    12 cm.
  • D
    10 cm.
4
The length of the side of a rhombus whose diagonals are of lengths 24 cm and 10 cm is
  • A
    13 cm.
    Correct
  • B
    14 cm.
  • C
    17 cm.
  • D
    16 cm.
5
If D is a point on side BC of \(\Delta ABC\)such that BD = CD = AD, then
Question 5 figure 1
  • A
    \(B{D^2} + A{D^2} = A{B^2}\)
  • B
    \(AB\;.\;AC = A{D^2}.\)
  • C
    \(C{D^2} + A{D^2} = A{C^2}\)
  • D
    \(A{B^2} + A{C^2} = B{C^2}\)
    Correct
6
In an equilateral \(\Delta ABC,\;AD \bot BC\;and\;A{D^2} = p.\;B{C^2},\)then p is equal to
  • A
    \(\frac{1}{3}\)
  • B
    \(\frac{1}{2}.\)
  • C
    \(\frac{3}{4}\)
    Correct
  • D
    \(\frac{2}{3}\)
7
In \(\Delta ABC,AB = 6\sqrt 3 \;cm,\;AC = 12\;cm\;and\;BC\; = \;6\;cm.\)The angle A and B are respectively
  • A
    \({45^0},{45^0}.\)
  • B
    \({60^0},{60^0}.\)
  • C
    \({30^0},{90^0}.\)
    Correct
  • D
    \({75^0},{30^0}.\)
8
If the length of a diagonal of a square is ‘a’, then its perimeter is
  • A
    2a.
  • B
    \(2\sqrt 2 a.\)
    Correct
  • C
    4a.
  • D
    \(\sqrt 2 a.\)
9
In \(\Delta PQR,\angle Q = {90^0},PQ = 5\;cm,\;QR = 12cm.\) If \(QS \bot PR,\) then QS is equal to
  • A
    \(\frac{{12}}{5}cm.\)
  • B
    \(\frac{{13}}{5}cm.\)
  • C
    \(\frac{{60}}{{13}}cm.\)
    Correct
  • D
    \(\frac{{80}}{{13}}cm.\)
10
In an isosceles triangle ABC, if AB = AC = 25 cm and BC = 14 cm, then the measure of the altitude from A on BC is
  • A
    22 cm.
  • B
    18 cm.
  • C
    24 cm.
    Correct
  • D
    20 cm.
11
In an equilateral triangle ABC if \(AD \bot BC,\) then \(A{D^2}\) is equal to
  • A
    \(2C{D^2}\)
  • B
    \(4C{D^2}.\)
  • C
    \(3C{D^2}.\)
    Correct
  • D
    \(C{D^2}\)
12
In the isosceles triangle ABC if AC = BC and \(A{B^2} = 2A{C^2}\) then the measure of \(\angle C\)is
  • A
    \({45^0}.\)
  • B
    \({60^0}.\)
  • C
    \({90^0}.\)
    Correct
  • D
    \({30^0}.\)
13
ABC is an isosceles triangle right-angled at B. Two equilateral triangles are constructed with side BC and AC as shown in figure. If \(ar(\Delta ACE) = 20\;c{m^2}\) then \(ar(\Delta BCD)\)is
Question 13 figure 1
  • A
    \(15\;c{m^2}.\)
  • B
    \(10\;c{m^2}\)
    Correct
  • C
    \(16\;c{m^2}.\)
  • D
    \(12\;c{m^2}.\)
14
In the given figure, the value of x is
Question 14 figure 1
  • A
    12 cm.
  • B
    6 cm.
  • C
    15 cm.
  • D
    10 cm.
    Correct
15
In the given figure ABC is a right-angled triangle right-angled at A. Semicircle are drawn on the sides of \(\Delta ABC.\) Then the area of the shaded region is equal to
Question 15 figure 1
  • A
    \(\frac{{ar(\Delta ABC)}}{2}\)
  • B
    \(\frac{{ar(semicircle\;BAC)}}{2}\)
  • C
    \(ar(semicircle\;BAC).\)
  • D
    \(ar(\Delta ABC)\)
    Correct