Question

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.

Answer 1

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

Answer 2

Thank you

Answer 3

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