Question

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?

Answer 1

The company can produce a maximum of 1,200 supports using the given metal stripping.

Step-by-step explanation:

To find the greatest possible number of supports that the company can produce, we need to determine how much metal stripping is needed to construct one support.

Each support is a right triangle with legs of length 3 feet and 4 feet, so the hypotenuse (third side) can be found using the Pythagorean theorem:

c² = a² + b²

c² = 3² + 4²

c² = 9 + 16

c² = 25

c = 5

Therefore, each support requires 5 feet of metal stripping.

With a total of 6,000 feet of metal stripping available and no waste, we can determine the maximum number of supports:

Number of supports = Total length of metal stripping ÷ Length of metal stripping per support

Number of supports = 6,000 ÷ 5

Number of supports = 1,200

Therefore, the greatest possible number of supports that the company can produce is 1,200.

Answer 2

The maximum number of supports that the company can produce is 500.

Step-by-step explanation:

Hi there!

First, let´s calculate how much material is needed to produce a single metal support. We know that the length of the legs is 3 and 4 feet respectively. Then, the length of the hypotenuse, according to the Pythagoras theorem, will be:

h² = L₁² + L₂²

Where:

h = hypotenuse.

L₁ = leg 1.

L₂ = leg 2.

Then:

h² = (3ft)² + (4ft)²

h² = 25 ft²

h = √(25 ft²)

h = 5 ft

Then each support will need (5 + 3 + 4) = 12 feet of metal stripping.

If the available material is 6000 ft, then the number of supports that can be produced will be (6000 ft / 12 ft/support) = 500 supports.