CAT 2025 Geometry & Mensuration Question (Hard)

Question

A triangle ABC is formed with AB AC 50 cm and BC 80 cm. Then, the sum of the lengths, in cm, of all three altitudes of the triangle ABC is

Accepted Answer

! image https optima-learn.b-cdn.net cat-pyq 2025 5eb8703e5af5e4c2.png The altitudes CM and BN will be equal as the triangle triangle ABC is isosceles. Further, in triangle AOB, using Pythagoras Theorem, we have AO 2 OB 2 AB 2, therefore, AO 2 50 2 - 40 2 Thus, AO 2 900 or AO 30 cm. We know that the

CAT 2025

Quantitative

Geometry & Mensuration

Hard

A triangle ABC is formed with AB = AC = 50 cm and BC = 80 cm. Then, the sum of the lengths, in cm, of all three altitudes of the triangle ABC is

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