CAT 2025 Slot 3 QA Question 21: 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

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

Since $AB = AC = 50$ and $BC = 80$, the altitude from $A$ to $BC$ bisects $BC$ into two segments of $40$ cm each.
$	ext{Altitude from A} = \sqrt{50^2 - 40^2}$
$= \sqrt{2500 - 1600} = 30$
$	ext{Area} = \dfrac{1}{2} 	imes 80 	imes 30 = 1200$
The altitude to each equal side is
$\dfrac{2 	imes 	ex

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

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