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?
+15001 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.
!
+1693 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 
