All categories

3 years ago

The perimeter of a triangle is not greater than 12 and the lengths of sides are natural numbers.

Mathematics

1 answer:

weqwewe [10]3 years ago

3 0

Answer:

3 triangles

Step-by-step explanation:

Perimeter of triangle = a + b + c

Given that :

P = 12

and a, b, c are natural numbers

Let :

Side A = a

Side B = b

Side C = 12 - (a + b)

Side A + side B > side C - - - (condition 1)

a + b > 12 - (a + b)

a + b > 12 - a - b

a + a + b + b > 12

2a + 2b > 12

2(a + b) > 12

a + b > 6

Side A - side B < side C

a - b < 12 - (a + b)

a - b + a + b < 12

2a < 12

a < 6

b < 6 (arbitrary point)

Going by the Constraint above :

The only three possibilities are :

(2, 5, 5)

(3, 4, 5)

(4, 4, 4)

Total number of triangle = 3

Equilateral triangle (all 3 sides equal) = (4, 4, 4) = 1

Isosceles triangle (only 2 sides equal) = (2, 5, 5) = 1

You might be interested in

A construction company built a scale model of a building. The model was built using a scale of 3 inches = 32 feet. If the buildi

Vlad1618 [11]

Let x represent the height of the model.

We have been given that a construction company built a scale model of a building. The model was built using a scale of 3 inches = 32 feet. We are asked to find the height of the model, if the building is expected to be 200 feet tall.

We will use proportions to solve our given problem as:

$\frac{\text{Model height}}{\text{Actual height}}=\frac{\text{Model length}}{\text{Actual length}}$

Upon substituting our given values, we will get:

$\frac{x}{200\text{ ft}}=\frac{3\text{ in}}{\text{32 ft}}$

$\frac{x}{200\text{ ft}}\times 200\text{ ft}=\frac{3\text{ in}}{\text{32 ft}}\times 200\text{ ft}$

$x=3\text{ in}\times 6.25$

$x=18.75\text{ in}$

Therefore, the model will be 18.75 inches tall.

7 0

3 years ago

Given the equation below, what is the value of 3 + 6(79 – s)? 7= -s+ 82

ss7ja [257]

Answer:

1 expression) 477 - 6s

2 equation) s = 75

Step-by-step explanation:

Also, the first expression is simplified

4 0

3 years ago

En una fábrica, dos trabajadores llenan envases de gel

mojhsa [17]

Responder:

Contenedor 24

Explicación paso a paso:

Para obtener la cantidad de contenedores que deberán llenar para completar sus respectivos paquetes al mismo tiempo; obtener el mínimo común múltiplo de la agrupación adoptada por el primer y segundo trabajador;

Múltiplos de:

8: 8, 16, 24, 32, 40, 48, 56, ...

12:12, 24, 26, 48, 60, ....

Por lo tanto, el mínimo común múltiplo de 8 y 12 es 24.

Llenarán 24 contenedores

4 0

3 years ago

-7x-3x+2=-8x-2 can you please show your work how

iVinArrow [24]

Answer:

x = 2

Step-by-step explanation:

Given

- 7x - 3x + 2 = - 8x - 2 ← simplify left side

- 10x + 2 = - 8x - 2 ( add 8x to both sides )

- 2x + 2 = - 2 ( subtract 2 from both sides )

- 2x = - 4 ( divide both sides by - 2 )

x = 2

8 0

3 years ago

1+3x=x+9 solve for x.. Help?

anzhelika [568]

Answer: x=4

Step-by-step explanation:

1+3x=x+9

-x -x

1+2x=9

-1 -1

2x=8

Divide by 2 on each side

Final result

x=4

7 0

3 years ago