A square and a rectangle have the same area. The length of the rectangle is five inches more than twice the length of the side of the square. The width of the rectangle is six inches less than the side of the square.

Find the length of the side of the square.

let's say that the side of the square is x. so the length of the rectangle is 2x+5 and the width is x-6. the area for squares and rectangles is a=bh and since the areas are the same we can equal the two areas to get to get ×^2=(2×+5)(×-6) after foiling you get x^2= 2×^2-7×-30 then subtract x^2 to both sides to get. 0=×^2-7×-30 so x = 3 and -10. because you can't have a negative side, the length of the side of the square is 3in.

Answered by Izzywombat | 2024-06-10

The length of the side of the square is 10 inches. This is found by setting up equations for the rectangle's dimensions based on the square's side, expanding the equations, and solving a quadratic equation. The valid solution is x = 10 because side lengths cannot be negative.
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Answered by Izzywombat | 2024-12-19