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 = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
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 = [tex]\sqrt{150(150-60)(150-100)(150-140)}[/tex]
= [tex]\sqrt{150(90)(50)(10)}[/tex]
= [tex]\sqrt{6750000}[/tex] ≈ 2598 units²
