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CAT Exam  >  CAT Questions  >  A triangle ABC has area 32 sq units and its s... Start Learning for Free
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
  • a)
    8 units
  • b)
    4 units
  • c)
    2√2 units
  • d)
    4√2 units
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A triangle ABC has area 32 sq units and its side BC, of length 8 units...
We know that area of the triangle = 32 sq. units, BC = 8 units
Therefore, the height of the perpendicular drawn from point A to BC = 2*32/8 = 8 units.
Let us draw a possible diagram of the given triangle.

We can see that if A coincide with (-4, 0) then the distance between A and (0, 0) = 4 units.
If we move the triangle up or down keeping the base BC on x = 4, then point A will move away from origin as vertical distance will come into factor whereas horizontal distance will remain as 4 units.
Hence, we can say that minimum distance between A and origin (0, 0) = 4 units.
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Most Upvoted Answer
A triangle ABC has area 32 sq units and its side BC, of length 8 units...
Let A be the point (0, y). Since BC lies on the line x=4, the x-coordinate of B is 4 and the x-coordinate of C is also 4.

The area of a triangle is given by the formula: Area = (1/2) * base * height.

In this case, the base of the triangle is BC, which has a length of 8 units. The height of the triangle is the y-coordinate of A, which we'll call h.

So, the area of the triangle is given by: 32 = (1/2) * 8 * h.

Simplifying the equation, we have: 32 = 4h.

Dividing both sides of the equation by 4, we have: h = 8.

So, the y-coordinate of A is 8.

The shortest distance between A and the point (0,0) is the length of the line segment connecting these two points, which is the distance formula: d = sqrt((x2-x1)^2 + (y2-y1)^2).

Substituting the coordinates of A and (0,0) into the distance formula, we have: d = sqrt((0-4)^2 + (8-0)^2).

Simplifying the equation, we have: d = sqrt(16 + 64) = sqrt(80) = 4*sqrt(5).

Therefore, the shortest possible distance between A and the point (0,0) is 4*sqrt(5) units.

So, the correct answer is: b) 4 units.
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Directions: Read the given information carefully and answer the question that follows.A spy of XYZ kingdom regularly spies between seven enemy camps that are located inside a forest, and are connected to each other by forest roads, FR–1, FR–2, FR–3, FR–4, FR–5, FR–6, and FR–7. The spy has made a map so that he can travel with ease between camps and get the useful information required. However, while travelling between any two enemy camps, the spy always chooses the route which passes through the minimum possible number of enemy camps. If two or more routes pass through the minimum number of enemy camps, he chooses the route for which the distance is also the least. The length of the forest road, directly connecting any two enemy camps, is a multiple of 10. For any pair of enemy camps, the length of a route connecting the two enemy camps and passing through the minimum possible number of enemy camps, is called a forest road stretch between the two enemy camps. The least among all the forest road stretches between two enemy camps is called the minimum forest road stretch between the two enemy camps.The following information is known about the distances between the enemy camps:1. The minimum forest road stretch between FR–4 and FR–6 is 90 miles, while the minimum forest road stretch between FR–2 and FR–6 is 30 miles.2. The highest forest road stretch between FR–1 and FR–7 is 360 miles.3. The minimum forest road stretch between FR–4 and FR–7 is 30 miles.4. The sum of the lengths of the road directly connecting FR–5 to FR–6 and that directly connecting FR–5 and FR–7 is 100 miles.5. The minimum forest road stretch between FR–7 and FR–2 is 70 miles, while the minimum forest road stretch between FR–3 and FR–7 is 110 miles.6. The length of the road directly connecting FR–3 and FR–6 is greater than 110 miles.7. The minimum forest road stretch between FR–1 and FR–4 is 110 miles, while the highest forest road stretch between FR–2 and FR–3 is 240 miles.The spys companion, Mr. Y, always travels along the shortest route when travelling from one enemy camp to another. On a particular day, both, the spy and Mr. Y, started from FR-1 and reached X, which is one of the other six enemy camps. If the length of the route that the spy took is greater than that of the route that Mr. Y took, how many of the six enemy camps were there in the route of the spy?

Directions: Read the given information carefully and answer the question that follows.A spy of XYZ kingdom regularly spies between seven enemy camps that are located inside a forest, and are connected to each other by forest roads, FR–1, FR–2, FR–3, FR–4, FR–5, FR–6, and FR–7. The spy has made a map so that he can travel with ease between camps and get the useful information required. However, while travelling between any two enemy camps, the spy always chooses the route which passes through the minimum possible number of enemy camps. If two or more routes pass through the minimum number of enemy camps, he chooses the route for which the distance is also the least. The length of the forest road, directly connecting any two enemy camps, is a multiple of 10. For any pair of enemy camps, the length of a route connecting the two enemy camps and passing through the minimum possible number of enemy camps, is called a forest road stretch between the two enemy camps. The least among all the forest road stretches between two enemy camps is called the minimum forest road stretch between the two enemy camps.The following information is known about the distances between the enemy camps:1. The minimum forest road stretch between FR–4 and FR–6 is 90 miles, while the minimum forest road stretch between FR–2 and FR–6 is 30 miles.2. The highest forest road stretch between FR–1 and FR–7 is 360 miles.3. The minimum forest road stretch between FR–4 and FR–7 is 30 miles.4. The sum of the lengths of the road directly connecting FR–5 to FR–6 and that directly connecting FR–5 and FR–7 is 100 miles.5. The minimum forest road stretch between FR–7 and FR–2 is 70 miles, while the minimum forest road stretch between FR–3 and FR–7 is 110 miles.6. The length of the road directly connecting FR–3 and FR–6 is greater than 110 miles.7. The minimum forest road stretch between FR–1 and FR–4 is 110 miles, while the highest forest road stretch between FR–2 and FR–3 is 240 miles.If the spy has to travel from FR-1 to FR-7, the distance (in miles) that the spy would have to cover is

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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) isa)8 unitsb)4 unitsc)2√2 unitsd)4√2 unitsCorrect answer is option 'B'. Can you explain this answer?
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