Question

In a right angled triangle one side is 8cm less than the hypotenuse and the other side is 1cm less than the first side, find all 3 sides?

Can someone please give me a step by step explanation. ​

Answer 1

Answer:

As the two larger numbers are differing by one, ONE of these is odd and the other is even. It is not possible to have THREE numbers where:-

(X x X) + (X + 7) x (X + 7) = (X + 8) x (X + 8) (i.e from Pythagorus’ theorem - the square on the hypotenuse = the sum of the squares on the two adjacent sides) where 2 numbers are even and one is odd.

Therefore x is odd, x+7 is even and x+8 is odd

Now for any given odd numbers greater than one, there is a formula for finding a Pythagorean triangle such that the given odd number is the shortest side, and the other sides differ by 1

Take the square of the odd number, and halve it. and round up and round down the two halves to give the two larger numbers.

The first few odd numbers give the following Pythagorean triangles

3,4,5

5,12,13

7,12,13

9,40,41

11,60,61

13,84,85

It is the SECOND of these sequences that gives the desired answer: 5,12,13

Step-by-step explanation:

Answer 2

Step-by-step explanation:

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