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A garden has the form of a right triangle. One leg of the triangle is formed by a 2400​-ft long sea wall. The hypotenuse of the triangle is 1600 ft longer than the other leg. What are the dimensions of the​ garden?

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sqdancefan

Answer:

  • given leg: 2400 ft
  • other leg: 1000 ft
  • hypotenuse: 2600 ft

Step-by-step explanation:

The Pythagorean theorem tells a relation between the leg lengths and the hypotenuse. If x represents the unknown leg length, then we have ...

  x^2 + 2400^2 = (x +1600)^2

  x^2 +5760000 = x^2 +3200x +2560000 . . . . eliminate parentheses

  3200000 = 3200x . . . . . . . . . subtract x^2+2560000

  1000 = x . . . . . . . . . . . . . . divide by 3200

The other leg length of the garden is 1000 ft. The garden is a triangle with side lengths 1000 ft, 2400 ft, 2600 ft.

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