High School

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You are making a triangular flag. The length of the flag is 4 inches greater than three times the base of the flag. There is enough material for a total area of 150 square inches.

What are the dimensions of the flag? (Round your answer to the nearest thousandth.)

What is the base of the flag?

Answer :

Final answer:

To find the dimensions of the flag, set up a system of equations based on the given information. Solve the equation to find the value of x, which will give us the base of the flag.

Explanation:

To find the dimensions of the flag, we can set up a system of equations based on the given information. Let's let the base of the flag be x inches. The length of the flag is 4 inches greater than three times the base, so the length of the flag is 3x + 4 inches. The area of a triangle is given by the formula 1/2 * base * height. In this case, the base of the flag is x inches and the height can be found by using the Pythagorean theorem. The height squared is equal to the length squared minus the base squared, so the height is sqrt((3x + 4)^2 - x^2). Now, we can set up an equation for the area of the flag. The area is given as 150 square inches, so we have 1/2 * x * sqrt((3x + 4)^2 - x^2) = 150. Solve this equation to find the value of x, which will give us the base of the flag.

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