Atriangle has a perimeter of 56 cm. each of the two longer sides of the triangle is three times as long as the shortest side. what is the length of each side of the triangle?

The lenght of each side is 24cm, 24cm, and 8cm.

In order to solve this problem, we know that the perimeter of a triangle equation is P = a + b + c, where a, b, and c are the sides of the triangle.

The perimeter is 56cm, we can write the equation as follow:

a + b + c = 56cm (1)

If each of the two longer sides of the triangles is three times as long as the shortest side, we can assume:

c = shortest side = x

a = b = longer sides = 3x

Substituting the values in the equation (1):

3x + 3x + x = 56cm

7x = 56cm

x = 56cm/7 = 8cm

c = shortest side = 8cm

a = b = longer sides = 3(8cm) = 24cm

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

the answer is 13 cm