Answer:
2598 units²
Step-by-step explanation:
Sum the parts of the parts of the ratio 3 + 5 + 7 = 15 parts
Divide the perimeter by 15
300 ÷ 15 = 20 ← value if 1 part, thus sides of triangle are
3 × 20 = 60
5 × 20 = 100
7 × 20 = 140
Using Hero's formula to calculate the area
A = 
where s is the semi perimeter and a, b , c are the sides of the triangle
s = 300 ÷ 2 = 150
let a = 60, b = 100 and c = 140, then
A = 
= 
= 
≈ 2598 units²
Let S, M, L represent the shortest, mid-length, and longest sides, respectively. You are given three bits of information.
.. S +M +L = 14.5 cm
.. L = 2S
.. L = 6.2 cm
You can use an equation something like this to find the middle-length side.
.. (6.2 cm)/2 +M +6.2 cm = 14.5 cm
.. M +9.3 cm = 14.5 cm . . . . . . . . . . . . . constant terms collected
.. M = 5.2 cm . . . . . . . . . . . . . . . . . . . . . subtract 9.3 cm
Now, you know the side lengths are 3.1 cm, 5.2 cm, 6.2 cm.
_____
You have not offered any choices for "which equation," so take your pick of those used here.
Times each side to get
2+2=3h^2
Then combine like terms.
4=3h^2
Then, Square root both sides
Meaning
2=3h
Your answer will be
2/3
