58432.Which of the following triangles have the same side lengths?
Scalene
Isosceles
Equilateral
None of these
Explanation:
Equilateral triangles have all sides and all angles equal.
58433.Area of an equilateral triangle with side length a is equal to:
$(\dfrac{\sqrt3}{2})a$
$(\dfrac{\sqrt3}{2}) a^2$
$(\dfrac{\sqrt3}{4}) a^2$
$(\dfrac{\sqrt3}{4})a$
Explanation:
Area of an equilateral triangle with side length a = $(\dfrac{\sqrt3}{4}) a^2
58434.D and E are the midpoints of side AB and AC of a triangle ABC, respectively and BC = 6 cm. If DE || BC, then the length (in cm) of DE is:
2.5
3
5
6
Explanation:
By midpoint theorem,
DE=$\dfrac{1}{2}$ BC
DE = $\dfrac{1}{2}$ of 6
DE = 3 cm
58435.The diagonals of a rhombus are 16 cm and 12 cm, in length. The side of the rhombus in length is:
20 cm
8 cm
10 cm
9 cm
Explanation:
Here, half of the diagonals of a rhombus are the sides of the triangle and side of the rhombus is the hypotenuse.
By Pythagoras theorem,
$(\dfrac{16}{2})^2+(\dfrac{12}{2})^2=side^2$
$8^2+6^2=side^2$
64+36=$side^2$
$side^2$ = 100
side=10 cm
58436.Corresponding sides of two similar triangles are in the ratio of 2:3. If the area of the small triangle is 48 sq.cm, then the area of large triangle
is:
230 sq.cm
106 sq.cm
107 sq.cm
108 sq.cm
Explanation:
Let A1 and A2 are areas of the small and large triangle.
Then,
$\dfrac{A2}{A1}$=($\dfrac{side \:\: of \:\: large \:\: triangle}{side \:\: of \:\: small \:\: triangle}$)
$\dfrac{A2}{48}=(\dfrac{3}{2})^2$
A2=108 sq.cm.
58437. If perimeter of a triangle is 100 cm and the length of two sides are 30 cm and 40 cm, the length of third side will be:
30 cm
40 cm
50 cm
60 cm
Explanation:
Perimeter of triangle = sum of all its sides
P = 30+40+x
100=70+x
x=30 cm
58438.If ABC and DEF are two triangles and $\dfrac{AB}{DE}=\dfrac{BC}{FD}$, then the two triangles are similar if
$\angle A=\angle F$
$\angle B=\angle D$
$\angle A=\angle D$
$\angle B=\angle E$
Explanation:
If ABC and DEF are two triangles and $\dfrac{AB}{DE}=\dfrac{BC}{FD}$, then the two triangles are similar if $\angle B=\angle D$.
58439.Which of the following are not similar figures?
Circles
Squares
Equilateral triangles
Isosceles triangles
Explanation:
All circles, squares, and equilateral triangles are similar figures.
58440.If in two triangles ABC and PQR, $\dfrac{AB}{QR} = \dfrac{BC}{PR} = \dfrac{CA}{PQ}$, then
ΔPQR ~ ΔCAB
ΔPQR ~ ΔABC
ΔCBA ~ ΔPQR
ΔBCA ~ ΔPQR
Explanation:
Given that, in triangles ABC and PQR, $\dfrac{AB}{QR} = \dfrac{BC}{PR} = \dfrac{CA}{PQ}$
If sides of one triangle are proportional to the side of the other triangle, and their corresponding angles are also equal, then both the
triangles are similar by SSS similarity. Therefore, ΔPQR ~ ΔCAB
58441.Which of the following is not a similarity criterion for two triangles?
AAA
SAS
SSS
ASA
Explanation:
The main criteria for similarity of two triangles are AAA, AA, SAS and SSS.
