Problem 1 :
The perimeter of an equilateral triangle is 24. What is the length of each altitude of the triangle ?
A) 4√3 B) 8√3 C) 4 D) 16
Solution :
Let ‘a’ be the side length of the equilateral triangle.
Perimeter of equilateral triangle = 24
3a = 24
a = 24/3
a = 8
By using Pythagorean theorem
AC^{2} = AD^{2} + DC^{2}
8^{2 }= 4^{2} + DC^{2}
64 = 16 + DC^{2}
DC^{2} = 64 - 16
DC^{2} = 48
DC = √48
= √(16 × 3)
= √(4 × 4 × 3)
= 4√3
So, the length of each altitude of the triangle = 4√3
So, option A) is correct.
Problem 2 :
The perimeter of an equilateral triangle is 12. What is the length of each altitude of the triangle ?
A) 2 B) 4√3 C) 2√3 D) 8
Solution :
Let ‘a’ be the side length of the equilateral triangle.
Perimeter of equilateral triangle = 12
3a = 12
a = 12/3
a = 4
By using Pythagorean theorem
AC^{2} = AD^{2} + DC^{2}
4^{2 }= 2^{2} + DC^{2}
16 = 4 + DC^{2}
DC^{2} = 16 - 4
DC^{2} = 12
DC = √12
= 2√3
So, the length of each altitude of the triangle = 2√3
So, option C) is correct.
Problem 3 :
The perimeter of an equilateral triangle is 18. What is the length of each altitude of the triangle ?
A) 6 B) 3√3 C) 6√3 D) 12
Solution :
Let ‘a’ be the side length of the equilateral triangle.
Perimeter of equilateral triangle = 18
So, 3a = 18
a = 18/3
a = 6
By using Pythagorean theorem
AC^{2} = AD^{2} + DC^{2}
6^{2 }= 3^{2} + DC^{2}
36 = 9 + DC^{2}
DC^{2} = 36 - 9
DC^{2} = 27
DC = √27
= 3√3
So, the length of each altitude of the triangle = 3√3
So, option B) is correct.
Problem 4 :
The perimeter of an equilateral triangle measures 30 cm. What is the length of the altitude?
A) 10√3 B) 5√3 C) 5 D) 5√2
Solution :
Let ‘a’ be the side length of the equilateral triangle.
Perimeter of equilateral triangle = 30 cm
So, 3a = 30
a = 30/3
a = 10
By using Pythagorean theorem
AC^{2} = AD^{2} + DC^{2}
10^{2 }= 5^{2} + DC^{2}
100 = 25 + DC^{2}
DC^{2} = 100 - 25
DC^{2} = 75
DC = √75
= 5√3
Length of each altitude of the triangle = 5√3.
So, option B) is correct.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM