Maths Questions

2009-10-14 2:35 am

1. The side of a aquare is 2 cm. Four triangles are cut from the corns of the square and a regular octagon (8-sided polygon) is formed. Find the length of each side of the cotagon.(Give the answer correct to 3 significat figures.)

2. A wire of length 60cm is cut into 2 parts. Each part is then bent to form a square. If the total area of the two squares is 117 cm2次, find the perimeter of each square.

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回答 (1)

Prof. Physics

2009-10-14 3:12 am

✔ 最佳答案

1. Let a be the length of one side of the triangle.

So, the length of the side of the octagon = (sqrt2)a

Therefore, a + a + (sqrt2)a = 2

a(2 + sqrt2) = 2

a = 0.586 cm

So, the length of each side of the octagon = (sqrt2)(0.586)

= 0.828 cm (3 sig. fig.)

2. Let a cm be the length of one part, then (60 - a) cm is the length of the other part

(a/4)2 + [(60 - a)/4]2 = 117

2a2 - 120a + 3600 = 1872

a2 - 60a + 864 = 0

(a - 36)(a - 24) = 0

a = 24 or 36

So, these are the lengths of the two parts, and also the perimeters of each square.

參考: Physics king

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