Question

If ABC is a right angle triangle with angle A = 90o and 2s = a + b + c, where a > b > c where notations have their usual meanings, then which one of the following is correct?

1)(s – b)(s – c) > s(s – a)

2)(s – a)(s – c) > s(s – b)

3)(s – a)(s – b) < s(s – c)

4)4s(s – a)(s – b)(s – c) = bc​

Answer 1

QUESTION :-

If ABC is a right angle triangle with angle A = 90o and 2s = a + b + c, where a > b > c where notations have their usual meanings, then which one of the following is correct?

1)(s – b)(s – c) > s(s – a)

2)(s – a)(s – c) > s(s – b)

3)(s – a)(s – b) < s(s – c)

4)4s(s – a)(s – b)(s – c) = bc

SOLUTION :-

➠ let a = 5 , b = 4 & c = 3 . satisfies the condition that a>b>c . these value form side of a right angle triangle because 3,4 and 5 is a Pythagoras triplets.

➠ s = a+b+c/2 = 12/2 = 6

➠ substitute these values and check which answer option hold good.

Choice (1) :- (s – b)(s – c) > s(s – a)

➠ LHS : (6-4)(6-3) = 2 × 3 =6

➠ RHS = 6(6-5) = 6 ×1 = 6

➠ .°. LHS=RHS is not greater than RHS.

➠ hence, choice (1) is not the answer.

Choice (2):- (s – a)(s – c) > s(s – b)

➠ LHS : (6-5)(6-3) = 1×3 = 3

➠ RHS : 6(6-4)= 6×2=12

➠.°. LHS=RHS is not greater than RHS.

➠ hence, choice (2) is not the answer.

Choice (3):- (s – a)(s – b) < s(s – c)

➠ LHS : (6-5)(6-4) = 1×4 = 4

➠ RHS : 6(6-3) = 6×3 = 18

➠.°. LHS=RHS are as stated in the answer choice.

ANSWER :- (3)