The sides of a right-angled triangle are 12 cm, 16 cm, 20 cm respectively. A new right angle Δ is made by joining the midpoints of all the sides. This process continues for infinite then calculate the sum of the areas of all the triangles so made.

A 312 sq.cm

B 128 sq.cm

C 412 sq.cm

D 246 sq.cm

Solution

Correct Answer: Option B

Area = \(\frac12\times12\times16\) =96

Sum of Area =\(\frac{96}{1-{\displaystyle\frac14}}\) = 128

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