Question : The sides of a triangle are 20 cm, 21 cm, and 29 cm. The area of the triangle formed by joining the midpoints of the sides of the triangle will be:
Option 1: $67 \frac{2}{3}$ cm2
Option 2: $52 \frac{1}{2}$ cm2
Option 3: $47 \frac{1}{2}$ cm2
Option 4: $58 \frac{1}{3}$ cm2
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Correct Answer: $52 \frac{1}{2}$ cm 2
Solution :
Given: The sides of a triangle = 29 cm, 21 cm, and 20 cm
We can see, $29^2 = 21^2 + 20^2$
So, this is a right-angled triangle.
⇒ Area $=\frac{1}{2}\times 21\times 20=210$ cm
2
Area of the smaller triangle $=\frac14\times210=\frac{105}{2}=52\frac12$ cm$^2$
Hence, the correct answer is $52\frac12$ cm$^2$.
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