Question

A triangle has a perimeter of 280 cm, and its side lengths are a, b and c respectively. If

Answer 1

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:

$a + b + c = 280$

a:b= 2:3

This means that:

$\frac{a}{b} = \frac{2}{3}$

$2b = 3a$

$b = \frac{3a}{2}$

b:c=4:5

This means that:

$\frac{b}{c} = \frac{4}{5}$

$4c = 5b$

$c = \frac{5b}{4}$

$c = \frac{5*3*a}{4*2} = \frac{15a}{8}$

At the original equation:

We replace b and c in function of a. So

$a + b + c = 280$

$a + \frac{3a}{2} + \frac{15a}{8} = 280$

Multiplying everything by 8

$8a + 12a + 15a = 280*8$

$35a = 280*8$

$a = \frac{280*8}{35}$

$a = 64$

Sides b and c:

Since we have a, we can find sides b and c:

$b = \frac{3a}{2} = \frac{3*64}{2} = 3*32 = 96$

$c = \frac{15a}{8} = \frac{15*64}{8} = 15*8 = 120$

The length of the sides are 64 cm, 96 cm and 120 cm.