# Mqs61qj Project 6

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MQS61QJ Project 6 1. A convex n-gon has 5 times as many diagonals as sides. Fully explain how to find the value of n. In order to find the value of n, I first found the number of diagonals in a convex n-gon by applying the formula (n(n-3))/2 in which n stands for the number of sides. In a convex polygon, the number of diagonals form from a single vertex is 3 less than the number of sides, which is represented as n-3. Moreover, since there are n sides, it would give n(n - 3) diagonals. However, each diagonal has 2 ends, in other words connecting from two vertices. As a result, each diagonal would be counted twice, thus n(n - 3) must be divided by 2. Since the convex n-gon has 5 times as many diagonals as sides, the formula can be equal to 5n. Therefore the new equation would be (n(n-3))/2=5n, and by multiplying both sides by 2, the equation would become n(n-3)=10n. Then, divide both sides…show more content…
Square SGRE has perimeter 24. Points H and N lie on SE and SG respectively, such that SH = SN. Segment XA is the reflection of HN in EG. The exact value of the perimeter of HEXAGN can be expressed as a – b*sqrt(c) where a, b, and c are positive integers. Find the values of a, b, and c. In order to find the length of each side of square SGRE, I divided the perimeter 24 by 4 because a square always has 4 sides. As a result, the length of each side of square SGRE is 6. Additionally, since SH = SN, I let the length of both segments be represented as the variable x. Not only that, the lengths of ¯AR and ¯XR also be represented as x because points X and A are the reflected points of points H and N in ¯EG respectively. Therefore, the lengths¯( HE), ¯EX, ¯AG, and ¯GN must be 6 – x. The exact value of the perimeter of HEXAGN can be expressed as a - b√c, thus I added all the sides of HEXAGN in terms of x. This was because the lengths of ¯AR, ¯XR, ¯SH, and ¯SN were still unknown, but it must be true that x stand for a positive integers due to a, b, and c being positive