Answer:
P = 36 cm. A = 36[tex]\sqrt{3}[/tex] sq. cm. or 60.62
Step-by-step explanation:
Equilateral triangle (all sides are =)
2b + 8 = 2a - b a + 5 = 2a - b
8 = 2a - 3b 5 = a - b
Solving as a system of equation
8 = 2a - 3b Do not change
5 = a - b Multiply by -3
8 = 2a - 3b
-15 = -3a +3b
7 = a
Solve for b: 8 = 2a - 3b
8 = 2(7) - 3b
8 = 14 - 3b
-6 = -3b
2 = b
What is the length of a side : 2(b) +8 = 2(2) + 8 ; 4 + 8 = 12
a + 5 = 7 + 5 = 12
2a - b = 2(7) - 2; 14 - 2 =12
P = 3 (sides); P = 3 (12); P = 36 cm.
A = 1/2bh , in this equilateral triangle the sides are 12 cm. So the base of the triangle is 12 and the height is 6[tex]\sqrt{3}[/tex]. ( draw the height from point A to the midpoint of CB, and you have a 60 30-90 Δ Long leg equal short leg [tex]\sqrt{3}[/tex]. A = 1/2 (12)(6[tex]\sqrt{3}[/tex]) ; A = 6(6[tex]\sqrt{3}[/tex]) ; A = 36[tex]\sqrt{3}[/tex] square cm
