The sides of a triangle ABC are AB = 5 cm, BC = 6 cm and CA = 7 cm, respectively
The sides of a triangle ABC are AB = 5 cm, BC = 6 cm and CA = 7 cm, respectively. Another triangle is formed by joining the mid-points of the sides of the triangle ABC. Find the perimeter of the second triangle in cm.
एक त्रिभुज ABC की भुजाएँ क्रमशः AB = 5 सेमी, BC = 6 सेमी तथा CA = 7 सेमी हैं। त्रिभुज ABC की भुजाओं के मध्य बिंदुओं को मिलाकर एक दूसरा त्रिभुज बनाया जाता है। दूसरे त्रिभुज का परिमाप (सेमी में) ज्ञात कीजिए।
Detailed Solution & Logic
9
In triangle ABC:
AB = 5 cm
BC = 6 cm
CA = 7 cm
Perimeter of triangle ABC
= $5 + 6 + 7 = 18$ cm
When the midpoints of the sides of a triangle are joined, a medial triangle is formed.
Each side of this new triangle equals half of the corresponding side of the original triangle.
So, perimeter of the new triangle
= $\frac{1}{2}$ × (perimeter of original triangle)
= $\frac{1}{2} \times 18 = 9$ cm
Correct Answer: 9
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