1) A vertical stick 20 metre long Casts a shadow 10 metre long on the ground. At the same time, a tower casts the shadow 50m long on the ground. Find the height of the tower. 100m
2) Two poles of height 6m and 11m stand vertically upright on a plane ground. If the distance between their foot is 12 metre. Find the distance between their tops. 13cm
3) In a right angle triangle, find the hypotenuse if base and perpendicular are respectively 36015 and 48020cm.
4) The perimeter of an equilateral triangle is 72√3 cm. Find its height.
36m
5) Find the area of a triangle with base 20cm and height 15cm. 150cm²
6) Find the area of a triangle whose base is 20cm and the corresponding services height is 4.6cm. 46 cm²
7) Find the area of the triangle whose sides are 3cm, 4cm and 5cm. Also, find the height of the triangle,
a) Corresponding to the longest side.
b) corresponding to the shortest side. 6cm², 2.4cm, 4cm
8) The base of a triangular field is three times its attitude. If the cost of cultivating the field at ₹38 per hectare is ₹513. Find its base and height. 300m, 900m
9) Find the area of a triangle whose sides are 42cm, 34cm and 20cm. Hence, find the height of the corresponding to the longest side.
336cm², 16 cm
10) Calculate the area of an equilateral triangle of side 12cm, correct to two decimal places. Also, find its height correct to one decimal places. (Take √3= 1.732) 62.35cm², 10.4 cm
11) Calculate the area of an equilateral triangle whose height is 6cm. (√3=1.73) 20.76cm²
12) The perimeter of an isosceles triangle is 42cm and base is 3/2 times each of equal sides. Find
a) The length of each side of the triangle. 18cm
b) area of triangle. 71.42cm²
c) height of the triangle. 7.94cm
13) The base of an isosceles triangle is 24cm and its area is 192cm². Find its perimeter. 64
14) The difference between the sides of a right angle triangle containing the right angle is 7cm and its area is 60cm². Calculate the perimeter of the triangle. 40
15) Find the area of the triangle whose sides are 30cm, 24cm and 18cm. Also find the length of the altitude corresponding to the smallest side of the triangle. 216cm², 24cm
16) The lengths of the sides of a triangle are in the ratio 3:4:5 and its perimeter is 144cm. Find the area of the triangle. 864cm²
17) The perimeter of a triangular field is 540m and its sides are in the ratio 25 :17: 12. Find the area of the triangle. Also, find the cost of cultivating the field at ₹24.60 per 100 m². 9000m², ₹2214
18) The base of a triangular field is twice its altitude. If the cost of cultivating the field at ₹14.50 per 100m² is ₹52200, find its base and altitude. 600m, 1200m
19) The perimeter of a right angled triangle is 60cm and it's hypotenuse is 25cm. Find the area of the triangle. 150cm²
20) Find the length of hypotenuse of an isoscles right angled triangle, having an area of 200cm² (√2=1.414). 28.28cm
21) Calculate the area and the height of an equilateral triangle perimeter is 60cm. 173.2, 17.32
22) Find the perimeter and area of an equilateral triangle whose height is 12 cm. Write your answers, correct to two decimal places. 41.57cm, 83.14cm²
23) The length of two sides of a right angle triangle containing the right angle differ by 2cm. If the area of the triangle is 24cm², find the perimeter of the triangle. 24
24) The sides of a right angled triangle containing the right angles are 5x cm 3x-1 cm. If its area is 60cm². find its perimeter. 40 cm
25) Each of the equal sides of an isosceles triangle is 2cm more than its height and the base of the triangle is 12cm. Find the area of a triangle. 48cm²
26) Find the area of an isosceles triangle, each of whose equal sides is 13cm and the base 24cm. 60cm²
27) The base of an isosceles triangle is 18cm and its area is 108cm². Find its perimeter. 48
28) If the area of an equilateral triangle is 81√3cm², find its perimeter. 54cm
29) The base of a right angled triangle is 24cm and its hypotenuse is 25cm. Find the area of the triangle. 84cm²
30) The altitude drawn to the base of an isosceles triangle is 8cm and the perimeter is 32 cm. Find the area of the triangle. 60cm²
31) The area of a triangle is 216cm² and its sides are in the ratio 3: 4:5 find the perimeter of the triangle. 72cm.
32) If the sides of a triangle are in the ratio of 1/2: 1/3: 1/4. The perimeter is 52cm, then the length of the smallest side is..
A) 12. B) 11 C) 8 D) none
33) The number of distinct triangles with Integral valued sides and perimeter as 14 is..
A) 2 B) 3 C) 4. D) 5
34) The sides of a triangle are 21, 20 and 13cm. Find the area of the larger triangle into which the given triangle is divided by the perpendicular upon the longest side from the opposite vertex. 96
35) The sides of the right angled triangle are 5 and 12 respectively. Find its hypotenuse. Find the perpendicular distance on hypotenuse. 13, 23/29
36) If the sides of a triangle measure 13, 14, 15 cm respectively, what is the height of the triangle for the base side 14,
A) 10 B) 12. C) 14 D) 13
37) If each side of an equilateral triangle is increased by 6cm, the area increased by 21√3 cm². Find the original side.
38) Find the two perpendicular sides of a right angle whose hypotenuse is 20cm and the area is 96cm². 16cm, 12cm
39) Let a, b, c be the length of the sides of triangle ABC Given (a+b+c)(b+c-a)= abc. Then the value of a will lie in between.
A) -1 and 1 B) 0 and 4
C) 0 and 1 C) 0 and 2 D) none
40) The numerical value of the product of the three sides (which are integers when measured in cm) of a right angled triangle having a perimeter of 56cm is 4200. Find the length of the hypotenuse. 25
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