NIMCET 2014 Mathematics PYQ — If and are three angles of a , whose area is . Let and be the sid… | Mathem Solvex | Mathem Solvex
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NIMCET 2014 — Mathematics PYQ
NIMCET | Mathematics | 2014
If A,B and C are three angles of a ΔABC, whose area is Δ. Let a,b and c be the sides opposite to the angles A,B and C respectively. If s=2a+b+c=6, then the product 31s2(s−a)(s−b)(s−c) is equal to:
Choose the correct answer:
A.
2Δ
B.
2Δ2
(Correct Answer)
C.
2Δ2
D.
Δ2
Correct Answer:
2Δ2
Explanation
Calculation:
Given s=2a+b+c=6
Area of the triangle is defined by Heron's Formula:
Δ=s(s−a)(s−b)(s−c)
Squaring both sides:
s(s−a)(s−b)(s−c)=Δ2
Multiplying both sides by s:
s×s(s−a)(s−b)(s−c)=s×Δ2
s2(s−a)(s−b)(s−c)=6Δ2
Multiplying both sides by 31:
31s2(s−a)(s−b)(s−c)=31×6Δ2
31s2(s−a)(s−b)(s−c)=2Δ2
Explanation
Calculation:
Given s=2a+b+c=6
Area of the triangle is defined by Heron's Formula:
