Answer:
A ≈ 1500[tex]\sqrt{3}[/tex] m²
Step-by-step explanation:
sum the parts of the ratio, 3 + 5 + 7 = 15 parts
Divide perimeter by 15 to find the value of one part of the ratio.
300 ÷ 15 = 20 m ← value of 1 part of the ratio , then
3 parts = 3 × 20 = 60 m
5 parts = 5 × 20 = 100 m
7 parts = 7 × 20 = 140 m
The 3 sides of the triangle are 60 m, 100 m , 140 m
To calculate the area (A) having all 3 sides use Hero's formula
A = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
where s is the semiperimeter and a, b , c the sides of the triangle
s = 300 m ÷ 2 = 150 m
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]
= [tex]\sqrt{10000}[/tex] × [tex]\sqrt{675}[/tex]
= 100 × [tex]\sqrt{25(27)}[/tex]
= 100 × 5[tex]\sqrt{27}[/tex]
= 500 × [tex]\sqrt{9(3)}[/tex]
= 500 × 3[tex]\sqrt{3}[/tex]
= 1500[tex]\sqrt{3}[/tex] m²
