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CAT 2018 Slot 2 — QA Question 15

TrianglesEasy

A triangle ABC has area 32 sq units and its side BC, of length 8 units, lies on the line x = 4. Then the shortest possible distance between A and the point (0, 0) is

Answer & solution

  • A

    8 units

  • 4 units

  • C

    2√2 units

  • D

    2√4 units

Solution

The area of the triangle is 32 sq units.

Therefore, 32 = ½ × BC × height

Given, BC = 8

⇒ Height =  2×328 = 8 cm

Therefore Height of the triangle = 8 cm.

Side BC lies on the line x = 4 or it is parallel to y-axis. Therefore the height of the triangle will be parallel to x axis. In order to minimize the distance of point A from the origin, point A should lie on the x-axis as shown.

Hence, point A is at a distance of 8 units from x = 4 and lies on x-axis.


Therefore point A is (-4,0) and the distance of point A from the origin = 4 units.

Hence, option (b).

CAT 2018 Slot 2 QA Q15: A triangle ABC has area 32 sq units and its side BC, of length 8 units, lies on the line x = 4. Then the short — Solution | TheCATExam