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Two triangles are similar. The smaller triangle has a perimeter of 2 units and an area of 2 square units. The perimeter of the larger triangle is 8 square units. What is the area of the larger triangle?

 Aug 14, 2021
 #1
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Two triangles are similar. The smaller triangle has a perimeter of 2 units and an area of 2 square units. The perimeter of the larger triangle is 8 units. What is the area of the larger triangle?

 

Hello Guest!

 

\(A_{sm}^2:A_{lg}^2=P_{sm}:P_{lg} \)

\(2^2:A_{lg}^2=2:8\\ 2A_{lg}^2=2^2\cdot 8\\ A_{lg}^2=\dfrac{2^2\cdot 8}{2}\\ A_{lg}= \sqrt{16}\)

\(A_{lg}=4\)

The area of the larger triangle is 4 square units.

laugh  !

 Aug 14, 2021
edited by asinus  Aug 14, 2021
 #2
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Such triangles are NOT possible!!!

 

For the given perimeter, the equilateral triangle has the largest area.

 

P = 3x (units)               A = 3x (square units)

 

x = 4√3 wink

civonamzuk  Aug 14, 2021

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