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Triangles

Theory and Formula


Questions


Q1. Can 12,5 and 13 be length of the sides of a right triangle?
(a) yes (b) no (c) can't say

Solution.
(a) yes
Longest side (13)2 = 169
Shorter sides (12)2 + (5)2 = 144 + 25 = 169
Solution

Q2. The difference of any two sides of a triangle is less than the third side.

(a) some time true (b) always true (c) false (d) can't say

Solution.
(b) always true
Solution

Q3. AB, AC and BC are the sides of a triangle, FC, BE and AD are the altitudes of a triangle. then

(a) AB + AC + BC = FC + BE + AD. (b) AB + AC + BC > FC + BE + AD.
(c) AB + AC + BC < FC + BE + AD. (d) None of these

Solution.
(b) AB + AC + BC > FC + BE + AD.
Note: The sum of three altitudes of a triangle is less than the sum of the three sides of a triangle .
Solution

Q4. D and E are the mid points of BC and AD respectively of ▵ABC. If area of ▵ ABC = 48cm2 find area of triangle EBD.


(a) 15cm2 (b) 12cm2 (c) 10cm2 (d) 24cm2

Solution.
(b) 12cm2
Solution

Q5. In a triangle ABC , DE ∥ BC find x, if AD = x, BD = x + 2, AE = x - 1, EC = x - 2.


(a) 2 (b)
3/2
(c)
2/3
(d) 3

Solution.
AD/DB
=
AE/EC

x/x + 2
=
x - 1/x - 2

x2 - 2x = x2 - x + 2x - 2
x =
2/3
Solution

Q6. In a triangle ABC, AD is the bisector of ∠A, AB = 8 cm, AC = 6 cm , BD = 4 cm, Aand DC = x cm


(a) 5 (b) 3 (c) 2 (d) 4

Solution.
AB/AC
=
BD/DC

8/6
=
4/x

x = 3 cm
Solution

Q7. ABC is a right triangle right - angled at B such that BC = 6 cm and AB = 8 cm . find the radius of its circle.

(a) 8 cm (b) 2 cm (c) 4 cm (d) 10 cm

Solution.


r = (AB + BC + AC)/2

r = (8 + 6 - 10)/2

= 4/2

r = 2
Solution

Q8. In a right triangle ABC, right angled at C. If tanB = 1 the 2 sinB . cosB = _______

(a) 4 (b) 3 (c) 1 (d) 2

Solution.
(c) 1
Solution

Q9. In a right triangle ABC, right angled at C. If tanB = 1 the 2 sinB . cosB = _______

(a) 4 (b) 3 (c) 1 (d) 2

Solution.
(c) 1
Solution

Q10. G is the centroid of the triangle of ABC . The area of the triangle ABC is 180 cm2. Find the area of the triangle GAC .

(a) 60 cm2 (b) 90 cm2 (c) 100 cm2 (d) 45 cm2

Solution.
(a) 60 cm2
Solution