In a right angled triangle, with hypotenuse c and legs a and b.
c^{2} = a^{2} + b^{2}
Note :
The hypotenuse is always the longest side and it is opposite the right angle.
Find x.
Problem 1 :
Solution :
The side which is opposite to right angle is 2x.
Hypotenuse = 2x
Using Pythagorean theorem :
(2x)^{2} = 12^{2} + x^{2}
4x^{2} = 144 + x^{2}
Subtract x^{2} on both sides, we get
3x^{2} = 144
Divide by 3 on both sides, we get
x^{2} = 144/3
x^{2} = 48
x = √48
Problem 2 :
Solution :
The side which is opposite to right angle is 13.
Hypotenuse = 13
Using Pythagorean theorem :
(13)^{2} = (3x)^{2} + (2x)^{2}
169 = 9x^{2} + 4x^{2}
169 = 13x^{2}
x^{2} = 169/13
x^{2} = 13
x = √13
Problem 3 :
Solution :
The side which is opposite to right angle is 3x.
Hypotenuse = 3x
Using Pythagorean theorem :
(3x)^{2} = x^{2} + (√24)^{2}
9x^{2} = x^{2} + 24
Subtracting x^{2 }on both sides, we get
8x^{2} = 24
Dividing by 8 on both sides, we get
x^{2} = 3
x = √3
Problem 4 :
Solution :
The side which is opposite to right angle is 4x.
Hypotenuse = 4x
Using Pythagorean theorem :
(4x)^{2} = (3x)^{2} + 7^{2}
16x^{2} = 9x^{2} + 49
Subtracting 9x^{2 }on both sides.
7x^{2} = 49
Dividing by 7 on both sides, we get
x^{2} = 49/7
x^{2} = 7
x = √7
Problem 5 :
Solution :
The side which is opposite to right angle is 3x.
Hypotenuse = 3x
Using Pythagorean theorem :
(3x)^{2} = (2x)^{2} + √15^{2}
9x^{2} = 4x^{2} + 15
Subtracting 4x^{2 }on both sides.
5x^{2} = 15
Dividing by 5 on both sides, we get
x^{2} = 15/5
x^{2} = 3
x = √3
Problem 6 :
Solution :
The side which is opposite to right angle is 5.
Hypotenuse = 5
Using Pythagorean theorem :
5^{2} = (3x)^{2} + (4x)^{2}
25 = 9x^{2} + 16x^{2}
25 = 25x^{2}
x^{2} = 1
x = 1
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM