Mathematics: A triangle has a perimeter of 280 cm, and its side lengths are a, b and c respectively. If a:b= 2:3, b:c=4:5, find the length of each side of the triangle.

None of them are polynomials except A...

A triangle has a perimeter of 280 cm, and its side

Ответ:

clarissajimenez27

25.03.2021

Mathematics

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.

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A triangle has a perimeter of 280 cm, and its side lengths are a, b and c respectively. If a:b= 2:3, b:c=4:5, find the length of each side of the triangle.

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A triangle has a perimeter of 280 cm, and its side lengths are a, b and c respectively. If a:b= 2:3, b:c=4:5, find the length of each side of the triangle.​

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A triangle has a perimeter of 280 cm, and its side lengths are a, b and c respectively. If a:b= 2:3, b:c=4:5, find the length of each side of the triangle.