Explanation

Since each support is in the shape of a right triangle with legs of length 3 feet and 4 feet, the length of the third side of the support is \(\sqrt{3^2 + 4^2}\), or 5 feet. The total length of the stripping of each support is therefore 3 + 4 + 5, or 12 feet. The company has 6,000 feet of metal stripping available. So, with no waste, the greatest possible number of supports that can be produced is \(\frac{6000}{12}\), or 500. The correct answer is Choice B.
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3,4,5 is the right angle triangle. So the number of 3,4,5 is the right angle triangles that can be formed from 6000 feet is 6000/12 = 500

Hi all,

Why do we add 3+4+5? I thought we determine the area of the triangle and then divide 6000 by that number?

What am I missing?

Thanks

I disagree with this one. If the legs of the table are 3 feet and 4 feet then the third side of the support would need to be screwed on as an attachment to the underside of the table. This means that the hypotenuse is 4 feet and the straight part of the table leg is 3 feet, and the missing section of the support is the square root of 16-9, which is the square root of 5. Therefore the answer would be 6000/(3+4+square root of 5). Without doing further calculations we know that the square root of 5 is between 2 and 3, so the answer is between 6000/9 and 6000/10 so it is between 600 and 666. None of the answers listed are correct. Otherwise the question needs to be rewritten to make clear that the 3 feet length is the base of the table, not the table leg itself.

That is why it is specifically mentioned that there is no loss of material, which is only possible if it is 3,4,5.

This is an easy one because they tell us that it's a right triangle and two of the legs equal 3 and 4. For right triangles with legs 3 and 4, the hypotenuse will be 5.

All we need to do is find the perimeter, which is 3 + 4 + 5 = 12. Then take the total amount of material and divide by the perimeter, 6000 / 12, which equals 500 supports.

Answer is B.

A construction company will produce identical metal supports in the shape of a right triangle with legs of length 3 feet and 4 feet. The three sides of each triangular support are to be constructed of metal stripping. If the company has a total of 6,000 feet of metal stripping and there is no waste of material in the construction of the supports, what is the greatest possible number of supports that the company can produce?

The metal support is in the shape of a right triangle of sides 3 and 4. Therefore the other side, the hypotenuse is 5 units long, 3-4-5 being well known pythagorean triplets.

The perimeter of the triangle-support is 3 + 4 + 5 = 12.

So each support requires 12 feet off metal stripping.

If the company has 6000 feet of metal, well we right away see that 12 x 5 = 60. So just add two more zeroes to 5 to get 500 triangle supports can be produced if there is no wastage.

Answer is B.
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