What is the area of right triangle ABC ?

Solution

Step 1: Analyse Question Stem

• ABC is a right triangle.
• Let us assume that in triangle ABC :

o Base = a
o Height = b
o And, hypotenuse = c

 \( a^2 + b^2 = c^2…..Eq.(i)\)
• We need to find the area of ABC

o i.e. we need to find the value of \( \frac{1}{2}*a*b\)

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

• According to this statement: c = 13
• However, we cannot find a and b from here, and hence cannot find the area.

• \(a + b + c = 30 ……Eq.(ii)\)
• We have 3 unknowns and only two equations (i.e. Eq.(i) and Eq.(ii)), so we cannot find the value of a and b.

Step 3: Analyse Statements by combining.

• From statement 1: c = 13
• From statement 2: a + b + c = 30
• On combining both statements , we get,

o \(a + b = 17 \)
o \(⟹ (a+b)^2 = 17^2\)
o \( ⟹ a^2 + b^2 +2a*b = 17^2\)
o \( ⟹ c^2 + 2*a*b = 17^2\) [ from Eq.(i)]
o \( ⟹ 2*a*b = 17^2 – 13^2 \)
o \( ⟹ \frac{1}{2}*a*b = \frac{17^2 – 13^2}{4}\)