Line, Angle and Triangle Page-3

17) Which of the following are not the sides of a right angled triangle?
(A) 3, 4, 5
(B) 1, √3, 2
(C) 1, 1, √2
(D) √3, √4, √5

View Answer

Answer: Option D

Solution:
(a) 32 + 42 = 252
(b) (1)2 + (√3)2 = (2)2
(c) (1)2 + (1)2 = (√2)2
(d) (√3)2 + (√4)2 ≠ (√5)2

18) What is the area of a square whose diagonal is 8?
(A) 16
(B) 64
(C) 32
(D) 24

View Answer

Answer: Option C

Solution:
triangle
If the measure of the side of square is x
x2+x2 = 64
2x2 = 64
x2 = 64/2 => 32
Area of square x2 = 32

19) In the figure below, what is the perimeter of ∆ABC
triangle
(A) 24
(B) 16
(C) 16+8√2
(D) 16+8√3

View Answer

Answer: Option A

Solution:
As m AB = m AC
m∠ B = m∠C
m∠B + m∠C = 180 - 60 = 120°
∴ m∠B = m∠C = 60°
∴ the three sides are equal mBC = 8
∴ the perimeter of the triangle = 8+8+8 = 24

20) For the triangle below, which of the following relationship between and b is true
(A) b = 60 - a
(B) a = b
(C) a + b = 90
(D) a = 90 - 3b

View Answer

Answer: Option A

Solution:
a + 2a + 3b = 180
3a + 3b = 180
a + b = 60
b = 60 - a

21) If the difference between the two acute angles of a right angled triangle is 8°, what is the measure of the smallest angle?
(A) 37°
(B) 41°
(C) 42°
(D) 49°

View Answer

Answer: Option B

Solution:
If the measures of the two acute angels are x and y where x > y then
x + y = 90 and x - y = 9
Adding, 2x = 98
x = 49
and y = 90 - 49 = 41
the measure of the smallest angle is 41°