NinetynineCAT 2025 Slot 3 QA Q1 Geometry
Question 1 of the Quantitative Ability (QA) section, CAT 2025 Slot 3, with CAT's official answer and a worked solution.
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
TITA: type in the answer. There are no options and no negative marking.
Answer: 126 Geometry TITA
Solution
- The altitude from \(A\) meets \(BC\) at its midpoint: \(h_A = \sqrt{50^2 - 40^2} = 30\).
- Area \(= \frac{1}{2}\times 80 \times 30 = 1200\).
- Altitudes to \(AB\) and \(AC\): \(\frac{2 \times 1200}{50} = 48\) each.
- Sum \(= 30 + 48 + 48 = 126\).
Shortcut. Every altitude is \(\frac{2\cdot\text{Area}}{\text{side}}\); find the area once.