1) Length of sides of triangles are 7cm, 24cm, 25cm. Triangle is
A) right angled triangle
B) isosceles triangle
C) Equilateral triangle
D) scalene triangle
2) Length of sides of triangles are 50cm, 80cm, 100cm. Triangle is
A) right angled triangle
B) isosceles triangle
C) Equilateral triangle
D) scalene triangle
3) Length of sides of triangles are 3cm, 8cm, 6cm. Triangle is
A) right angled triangle
B) isosceles triangle
C) Equilateral triangle
D) scalene triangle
4) Length of sides of triangles are 13cm, 12cm, 5cm. Triangle is
A) right angled triangle
B) isosceles triangle
C) Equilateral triangle
D) scalene triangle
5) Length of sides of triangles are 1.4cm, 4.8cm, 5cm. Triangle is
A) right angled triangle
B) isosceles triangle
C) Equilateral triangle
D) scalene triangle
6) An aeroplane leaves an airport and flies due to North at a speed of 1000km per hour. At the same time, another aeroplane leaves the same airport and flies due to West at a speed of 1200 kmph. How far apart will be the two planes after 3/2 hours?
A) 100 B) 100√6 C) 100/√6 D) 300√61
7) For going to a city B from city A, there is route via city C such that AC perpendicular to CB, AC= 2x km and CB = 2(x+7) km. It is proposed to construct a 26km highway which directly connects the two cities A and B. Find how much distance will be saved in reaching city B from city A after the construction of highway.
A) 8 B) 10 C) 20 D) 12
8) A 5m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4m high. If the foot of the ladder is moved 1.6m towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall.
A) 0.4 B) 0.6 C) 0.8 D) 0.10
9) ABC is an equilateral triangle of side 2a. Find each of its altitude.
A) a B) √a C) 2√a D) √3 a
10) Foot of a 10m long ladder leaning against a vertical wall is 6m away from the base of the wall. Find the height of the point on the wall where the top of the ladder reaches.
A) 4m B) 6m C) 8m D) 10m
11) A guy attached a wire 24m long to a vertical pole of height 18m and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taught?
A) 6 B) 7 C) 7√6 D) 6√7
12) Two poles of height 6m and 11m stand on a plane ground. If the distance between their feet is 12m, find the distance between their tops.
A) 11 B) 12 C) 13 D) 14
13) In a right angled triangle, if hypotenuse is 20cm and the ratio of the other two sides is 4:3, find the sides.
A) 16, 12 B) 12, 14 C) 14, 18 D) 12, 18
14) If the sides of a triangle are in 3:4:5, then the triangle is;
A) right angled triangle
B) isosceles triangle
C) Equilateral triangle
D) scalene triangle
15) The hypotenuse of a right angled triangle is 6m more than twice the shortest side. If the third side is 2m less than the hypotenuse, find the sides of the triangle.
A) 10,24,26 B) 12,24,26 C) 12,24,28 D) none
16) In ∆PQR PD perpendicular to QR, such that D lies on QR. If PQ= a, PR= b, QD= c and DR= d then find the value of (a+ b)(a - b).
A) (c+ d)(c - d) B) (c- d)(c + d)
17) ABC is an isosceles with AB= AC= 12 and BC= 8cm. Find the altitude on BC and hence calculate its area.
A) 8, 32 B) 8√2, 32 C) 8, 32√2 D) 8√2, 32√2
18) Find the area and the perimeter of a square whose diagonals is 10cm long.
A) 50, 20 B) 50√2, 20 C) 50, 20√2 D) 50√2, 20√2
19) In ∆ABC, AB= AC=x, BC= 10cm and the area of ∆ABC is 60cm². Find x.
A) 10 B) 12 C) 13 D) 14
20) In a rhombus, if diagonals are 30cm and 40cm, find its perimeter.
A) 100 B) 8√2 C) 32√2 D) 110
21) In a ∆ABC, AB= 6√3, BC= 6 and AC= 12cm, then angle B is
A) 120° B) 90° C) 60° D) 45°
22) If the sides of a rectangular plot are 15m and 8m, then the length of its diagonal is
A) 17m B) 23m C) 21m D) 17cm
23) If a side of a rhombus is 10cm and one of the diagonals is 16cm, then the length of the other diagonals is
A) 6cm B) 12cm C) 21m D) 17cm
24) If a ladder 10m long reaches a window 8m above the ground, then the distance of the foot of the ladder from the base of the wall is
A) 18m B) 8m C) 6m D) 4m
25) A girl walks 200 towards East and then she walks 150m towards North. The distance of the girl from the starting point is
A) 350m B) 250m C) 300m D) 225m
26) A ladder reaches a window 12m above the ground on one side of the street, keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 9m high. If the length of the ladder is 15m, then the width of the street is
A) 30m B) 24cm C) 21m D) 18m
27) In a triangle ABC, AD perpendicular to BC, AB= 25cm, AC = 17cm and AD= 15cm. Find the length of BC. 28cm
28) ∆ABC is a right angled triangle at B. Given that AB= 9cm, and AC = 15cm and D,E are the midpoint of the sides AB and AC respectively, Calculate
i) the length of BC.
A) 12cm B) 14cm C) 16cm D) 20cm
ii) the area of ∆ADE.
A) 12m² B) 13.5cm² C) 21.5m² D) n
29) Which of the triangle whose sides are given below are right angled?
a) 5,12,13
b) 6,8,10
c) 24,10,26
d) 7,24,25
e) 8,15,17
f) 8,10,11
g) 8,40,41
h) 36,15,39
i) 16,63,65
30) A right angled triangle has hypotenuse of length p cm and one side of length q cm. If p - q=1, find the length of the third side of the triangle.
31) In ∆ ABC, BC= 12cm, CA=16cm and AB= 20 cm. Find the value of angle C.
32) In ∆ ABC, AD perpendicular to BC, AD= BD= 5cm, BC= 17cm. Find the value of AC.
33) The foot of a ladder is at a distance of 8 m from the wall of a house and the top of the ladder is at the height of 15m from the ground. Find the length of the ladder .
34) A ladder 13m long reaches a window of a building 12 m above the ground. Determine the distance of the foot of the ladder from the building.
35) The heights of two vertical pillars are 7m and 12m. The distance between their feet is 12m. Find the distance between their tops.
36) A man goes 15m due east and then 8m due North. How far is he from the starting point ?
37) In ∆ ABC is right angled at A. AD perpendicular to BC. If BC=1.25m, AB= 1m, Find AD.
38) In the following figure, ABC is a right angled triangle at B. AD and CE are the two median drawn from A and C respectively.
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