Cannon wants to make a garden with a border of his yard. He has lumber in several different lengths. Which three lengths could be used to make a right triangle to fit into the corner of his yard?
A. 4ft.,6ft.,10ft.
B.7ft.,12ft.,15ft.
C.5ft.,12ft.,13.
D.10ft.,15ft.,20.
C as the square of 12 and 5 is equal to square of 13 , as per Pythagoras theorem , in a right angled triangle, the sum of the squares of the two sides forming the right angle is equal to the square of the hypotenuse
Thank you
A triple of numbers such as 5, 12, 13 is called a Pythagorean triple, because the satisfy the Pythagorean equation.
The simplest such triple is 3, 4, 5
(3^2 + 4^2 = 5^2)
and 5, 12, 13 is the next simple one.
Of course any multiple of that triple would also work, e.g. 3 x (3, 4, 5) --- > 9, 12, 15
You will find it beneficial to memorize these two basic ones, it will come in handy for many questions of this type
To determine which three lengths could be used to make a right triangle, we need to check if the Pythagorean theorem holds true. According to the theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's test each option:
A. 4ft., 6ft., 10ft.
In this case, 4² + 6² = 16 + 36 = 52, which is not equal to 10² = 100. Therefore, option A does not form a right triangle.
B. 7ft., 12ft., 15ft.
Here, 7² + 12² = 49 + 144 = 193, which is not equal to 15² = 225. Hence, option B does not form a right triangle either.
C. 5ft., 12ft., 13ft.
For this option, 5² + 12² = 25 + 144 = 169, which is equal to 13² = 169. Therefore, option C forms a right triangle.
D. 10ft., 15ft., 20ft.
In this scenario, 10² + 15² = 100 + 225 = 325, which is not equal to 20² = 400. Thus, option D does not form a right triangle.
Therefore, the three lengths that can be used to make a right triangle to fit into the corner of the yard are C. 5ft., 12ft., 13ft.