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?

Guest Aug 14, 2021

#1**+1 **

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.

!

asinus Aug 14, 2021

#2**0 **

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 **

civonamzuk
Aug 14, 2021