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
Explanation:
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).
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