By using Pythagorean theorem, we can determine whether the three sides will create a right triangle.
a^{2} = b^{2} + c^{2}
Here the longest side can be considered as hypotenuse. We have to check, if the square of the longest side is equal to the some of squares of the remaining sides.
The following figures are not drawn to scale. Which of the triangles are right angled?
Problem 1 :
Solution :
Using
Pythagorean theorem.
7^{2} = 4^{2} + 5^{2}
49 = 16 + 25
49 ≠ 41
So, it is not a right triangle.
The following figures are not drawn to scale. Which of the triangles are right angled?
Problem 2 :
Solution :
The measure of longest side = 15
a = 15, b = 12 and c = 9
Using Pythagorean theorem.
15^{2} = 12^{2} + 9^{2}
225 = 144 + 81
225 = 225
So, it is a right triangle.
Problem 3 :
Solution :
The measure of longest side = 9 cm
a = 9, b = 8 and c = 5
Using Pythagorean theorem.
9^{2} = 8^{2} + 5^{2}
81 = 64 + 25
81 ≠ 89
So, it is not a right triangle.
Problem 4 :
Solution :
The measure of longest side = √12
a = √12, b = √7 and c = 3
Using Pythagorean theorem.
(√12)^{2} = (√7)^{2} + 3^{2}
12 = 7 + 9
12 ≠ 16
So, it is not a right triangle.
Problem 5 :
Solution :
The measure of longest side = √75
a = √75, b = √48 and c = √27
Using Pythagorean theorem.
(√75)^{2} = (√48)^{2} + (√27)^{2}
75 = 48 + 27
75 = 75
So, it is a right triangle.
Problem 6 :
Solution :
The measure of longest side = √75
a = √75, b = √48 and c = √27
Using Pythagorean theorem.
17^{2 }= 15^{2} + 8^{2}
289 = 225 + 64
289 = 289
So, it is a right triangle.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM