Question

An quadrilateral triangle has sides of length 25 CM if the side of triangle is increased by 30% then find what fraction of the perimeter of the new triangle is perimeter of previous triangle ?

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Answer 1

Prove by principal of Mathematical Induction that, 1+3+5+……….+(2n- 1) = n 2 iv) If z = x + i y and | 2z-1|= |z-2|, prove that , x 2 + y 2 = 1

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Answer 2

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There are 2 components to this problem. The first, and easier one, is recognizing how much of the perimeter the equilateral triangles take up—since there are 40 triangles in total, there must be 40 – 4 = 36 of these triangles. By observation, each contributes only 1 side to the overall perimeter, thus we can simply multiply 36(5) = 180" contribution.

The second component is the corner triangles—recognizing that the congruent sides are adjacent to the 5-inch equilateral triangles, and the congruent angles can be found by

180 = 30+2x → x = 75°

We can use ratios to find the unknown side:

75/5 = 30/y → 75y = 150 → y = 2''.

Since there are 4 corners to the square rug, 2(4) = 8'' contribution to the total perimeter. Adding the 2 components, we get 180+8 = 188 inch perimeter.

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