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The area of a rectangle is 520 square inches. The length is 3 more than twice the width. The equation 520 = 2w2 + 3w can be used to find the length and width of the rectangle.

Josiah wants to build a rectangular rose garden against the back of his house with a fence around it, but he only has 120 feet of fencing available. He wants to find the dimensions (length and width) of the garden (with one side attached to the house) to make the area of the garden as large as possible. To find the max area, he will need to find the vertex of the area equation A = 60w − w2

The hypotenuse of a right triangle is 4 inches longer than one leg and 2 inches longer than the other. The equation x2 − 4x − 12 = 0 can be used to find the dimensions of the triangle.

The product of two consecutive even whole numbers is 1088. The equation n(n + 1) = 1088 can be used to find the numbers.