<span>Given: width = x - 1 P = 4x + 6 What is area, A? ... We need to again determine the length of the other side (in this case, the Length), in terms of x .... P = 2 w + 2 L P = 2 (x - 1) + 2 ( L) = 4x + 6 ... subtract 2x - 2 from both sides: 2 (L) = 4x + 6 - (2x -2) 2 (L) = 2x + 8 ... divide both sides by 2: L = x + 4 ... Now we know both sides: w = x - 1 (given) L = x + 4 (calculated) ... To determine the Area, A, we just multiply the two sides together: A = (x - 1) (x + 4) A = x^2 - 1x + 4x - 4 </span><span>A = X^2 + 3x - 4</span><span>This is actually two problems. ... First one: ... Let A = area, which is short side (width) x long side (length) Given, A = 6x^2 + 5x + 1 Given one side = 3x + 1 (we don't know if this the width or length) ... If A = side x side, and we are given A and one side, we can divide A by the given side to derive the remaining (unknown) side: ... Since A is in the form of a quadratic equation, if we factor it, the two factors are the equations in terms of x for each of the two sides: ... (3x + 1) (?x + ??) = 6x^2 + 5x + 1 (3x + 1) (2x + 1) are the two factors and thus, are the two sides. The missing side we needed to solve for is: ... 2x + 1 ... However, we are asked for its perimeter in terms of x. The equation for P, the perimeter, is: P = 2 x width + 2 x length ... We already determined the width = 2x + 1 We were given length = 3x + 1 ... P = 2 (2x + 1) + 2 (3x + 1) P = 10x + 4 </span>
