A piece of paper in the shape of an isosceles right triangle is cut...

Solution

Step 1: Analyse Question Stem

• Triangle is an isosceles right-angle triangle

o Base = perpendicular = x(say)
o Area = \(\frac{1}{2} *x*x\)
o \(25 = \frac{1}{2}*x^2\)

 \(x = \sqrt{50} =5\sqrt{2}\)
o Hypotenuse = 10

o We need to find any of the side after the cut.

 After all it's goining to be an isosceles right-angled triangle only

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

• Now, simply BD is a perpendicular of AC, and it will divide the AC into two equal parts

o BDC is a right-angled triangle

 \(BC = 5*\sqrt{2}, CD = 5\)
• \(BD = 5\)

o Now, \(BM = 5-2 = 3\)

 \(EM =MF = BM = 3\) [EBF is an isoceles right angled triangle]
 Now, \(EF = EM + MF = 3+ 3 = 6\)
 This is the hypotenuse of new triangle.
o Thus, we can find the area.

• New hypotenuse = \(10 – \frac{10}{100}*40 = 10 – 4 = 6\)

o Thus, we can find the area of new triangle.