Star - Part 2

Geometry Level 1

The above image shows a 5-pointed star ABCDE, and a regular pentagon FGHIJ.

If AHI has perimeter 10, what is the length of DE?

10 5 12 15

Chung Kevin by Chung Kevin , 45, Australia

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4 solutions

Note that A H = A I = D G = F E AH=AI=DG=FE and I H = G F IH=GF , therefore the perimeter of triangle A H I AHI is eqaul to the length of D E DE and that is 10 10 units.

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Assuming the two sides of the triangle to be equal and there value be equal to 3. And the base of the triangle is also a side in the regular pentagon. Since the perimeter of AHI=10 We can compute as 3+3+4=10. Assuming the base side to have a value of 4. Then the length of the triangle would be 4+3+3=10, since visually the triangles look alike.

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Azadali Jivani
Aug 4, 2015

perimeter of Triangle AHI = 10
so HI = 10/3 =DG = FE
so DE = 10/3+10/3+10/3 = 10 (Ans.)

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Paola Ramírez
Jul 15, 2015

Perimeter of △ A H I = \triangle AHI= length of D E DE

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Can you explain further?

Chung Kevin - 5 years, 10 months ago

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there are 2 side legths and a base length, Same as there is for the triangle. Triangle parimeter =10 so does the line length.

michael bye - 5 years, 10 months ago

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