Question

the sides of a right angle triangle are in the automatic progression if the triangle has area 24 then what is the length of its smallest side ?​

Answer 1

Answer:

6 is the smallest side .

Step-by-step explanation:

We are given that the sides are in airthematic progression .

• By using the fact that any 3 numbers which are in A.P are of form

▶ a - d , a , a + d

here, a is the first term and "d" is the common difference of the A.P

▶ Now, apply the formula of area of traingle

= 1/2 × (base) × (height)

=> 1/2 ( a - d ) (a ) = 24

( a - d ) (a ) = 48 ...............(i)

Now , we can use hit & trail method

Factors of 48 are :

2, 2, 2, 2, 3

Now , we want to get 48

so , possible numbers are 6 and 8 which satisfy the (i) relation .

▶ a = 8

▶ d = 2

•°• Verification :-

( 8-2)(8) = 48

(6)(8) = 48

Now, the smallest from a - d , a , a + d is (a - d )

So , the Smallest side is 6