Answer:
The length of the sides are 64 cm, 96 cm and 120 cm.
Step-by-step explanation:
Perimeter of a triangle:
The perimeter of a triangle is the sum of it's sides.
A triangle has a perimeter of 280 cm, and its side lengths are a, b and c respectively.
This means that:
[tex]a + b + c = 280[/tex]
a:b= 2:3
This means that:
[tex]\frac{a}{b} = \frac{2}{3}[/tex]
[tex]2b = 3a[/tex]
[tex]b = \frac{3a}{2}[/tex]
b:c=4:5
This means that:
[tex]\frac{b}{c} = \frac{4}{5}[/tex]
[tex]4c = 5b[/tex]
[tex]c = \frac{5b}{4}[/tex]
[tex]c = \frac{5*3*a}{4*2} = \frac{15a}{8}[/tex]
At the original equation:
We replace b and c in function of a. So
[tex]a + b + c = 280[/tex]
[tex]a + \frac{3a}{2} + \frac{15a}{8} = 280[/tex]
Multiplying everything by 8
[tex]8a + 12a + 15a = 280*8[/tex]
[tex]35a = 280*8[/tex]
[tex]a = \frac{280*8}{35}[/tex]
[tex]a = 64[/tex]
Sides b and c:
Since we have a, we can find sides b and c:
[tex]b = \frac{3a}{2} = \frac{3*64}{2} = 3*32 = 96[/tex]
[tex]c = \frac{15a}{8} = \frac{15*64}{8} = 15*8 = 120[/tex]
The length of the sides are 64 cm, 96 cm and 120 cm.
