Question

If the sides of a right ∆ are a , a + 1 and a - 1, then the length of the hypotenuse is ( 'a' is a positive integer > 1 )

Answer 1

Answer:

GIVEN: A triangle ABC right angled at A, AC = 12, AB = s & hypotenuse BC = h

TO FIND: greatest possible perimeter

By Pythagoras law:

h² = s² + 12²

=> 144 = h² - s²

=> 144 = (h-s) ( h+s)

=> 144 = 1 * 144

or, 144 = 2 * 72

or, 144 = 3 * 48

or, 144 = 4 * 36

or, 144 = 5 * 28.8 …………….& so on

If we take the above factors of 144 in non integral form, s & h will also be in non integral form.

Here, we need highest perimeter,

So, highest value of h+s is 144. Then next is 72….. & so on..

So, h - s = 1

h+ s = 144

=> 2h = 145

=> h = 72.5

=> s = 71.5

So, highest possible perimeter

= 72.5 + 71.5 + 12 = 156… But these values are ruled out, as sides are in integral form.

So, we take next set ofvalues

h+s = 72

h- s = 2

=> 2h = 74

=> h = 37

=> s = 72- 37 = 35

So, sides are to be 12, 35, & 37

Highest possible perimeter = 84

Answer 2

Answer:

as no values  are given we can compare the variable values

1st side = a

2nd side = a+1

3rd side = a-1

a-1 < a < a+1

we know - longest side is the hypotenuse

therefore a+1 is the ans

Step-by-step explanation: