Question

The square of a number 'A' is the sum of the square of other two numbers 'B' and 'C'. Where 5B = 12C and B,C are positive numbers. The least possible positive value of A is: (a) 10 (b) 12 (c) 13 (d) 16

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Answer 1

Option (C)

Given :-

♦ The square of a number 'A' is the sum of the squares of other two numbers 'B' and 'C'.

♦ Where 5B = 12C and B,C are positive numbers.

To find :-

♦ The least possible positive value of A .

Solution :-

Given that

A, B and C are the three positive numbers.

The square of a number 'A' is the sum of the squares of other two numbers 'B' and 'C'.

=> A² = B²+C² -------------(1)

and

5B = 12C

=> B/C = 12/5

=> B : C = 12:5

Let B = 12X and C = 5X

Now,

(1) becomes

=> A² = (12X)² + (5X)²

=> A² = 144X² + 25X²

=> A² = (144+25)X²

=> A² = 169X²

=> A = ±√(169X²)

=> A = ±13X

=> A = 13X

Since, A,B and C are positive numbers.

We have, A = 13X

=> A = Multiple of 13

If we substitute X = 1,2,3... then We get

A = 13, 13×2 , 13×3,...

=> A = 13,26,39,...

The least value of A = 13

Answer :-

♦ The least possible positive value of A = 13

Answer 2

• please check the attached file