Q1.
The areas of two similar triangles are in respectively 16 cm2 and 25 cm2. The ratio of their corresponding sides is.
(a) 2:1 (b) 3:2 (c) 4:3 (d) 4:5
Solution.
(d) 4:5
Note : The ratio of the areas of two similar triangles is equal to the ratio of the squares of any two
corresponding sides.
Solution
Q2.
Two triangles have equal angles and their areas are in the ratio 16:25. The ratio their corresponding heights is.
(a) 4:5
(b) 2:3 (c) 1:2 (d) 3:4
Solution.
(a) 4:5
Solution
Q3.
Two triangles are similar if their corresponding angles are equiangular.
(a) True (b) False (c) Can't say
(d) Not relation
Solution.
(a) True
Solution
Q4.
The perimeters of two similar triangles are 30 cm and 25 cm respectively . If one side of first triangle is 8 cm. What is the corresponding
side of the other triangle ?
(a) 10/3 (b) 3 (c) 20/3 (d) 20
Solution.
30/25 = 8/x
6/5 = 8/x
6x = 40
3x = 20
x = 20/3
Solution
Q5.
A right triangle has hypotenuse of length p cm and other side of length q cm. If p - q = 2 cm . find the length of the third side.
(a) √1 + p (b) √1 + q (c) 2 (d) 2√1 + q
Solution.
Using pythagoras theorem ,
let third side is x cm.
p2 = q2 + x2
x2 =
p2 - q2 = (p - q)(p + q) = 2(p + q)
p - q = 2
p = 2 + q
x = √ 2(p + q)
x = √2(2 + q + q)
x = √2(2 + 2q)
x = 2√(1 + q)
Solution
Q6.
P and Q are the mid - points of the sides CA and CB respectively of a triangle of ABC, right angled at C. AB = 5 cm, AC = 4 cm and BC = 3 cm.
find AQ
(a) (√74)/4 (b) 2 (c) 4 (d) √14
Solution.
We know that 4AQ
2 = 4AC
2 + BC
2 AQ
2 =
4AC2 + BC2/4
AQ
2 =
4 x 16 + 9/4
=
64 + 9/4
=
74/4
AQ = √
74/4
Solution
Q7.
What is the distance between two parallel tangents of a circle of radius 6 cm ?
(a) 6 (b) 12 (c) 3 (d) 13
Solution.
(b) 12
Solution
Q8.
The length of the tangent from a point A at a circle, of radius 3 cm, is 4 cm. The distance of A from the centre of the circle is.
(a) 5 (b) 3 (c) 4 (d) 2
Solution.
(a) 5
Solution
Q9.
In the figure, if AB = 12 cm, BC = 8 cm and AC = 10 cm then AF = ______.
(a) 2 (b) 3 (c) 7 (d) 5
Solution.
(c) 7
x + y = 12
y + z = 8
x + z = 10
x + y = 12
- y + z = 8
x - z = 4
x + z = 10
x - z = 4
2x = 14
x = 7
x + y = 12
y = 5
y + z = 8
5 + z = 8
z = 3
x = 7, y = 5, z = 3
Solution
Q10.
If an isosceles triangle ABC in which AB = AC = 6 cm is inscribed in a circle of radius 9 cm, find the area of the triangle.
(a) 8√2 cm2 (b) 6√2 cm2 (c) 8 cm2 (d) 6cm2
Solution.
(a) 8√2 cm2
Solution
