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3 years ago

14

A triangle has one side length of 12 inches and another of 8 inches. Describe all possible lengths of the third side. Show and e

xplain your reasoning.

2 answers:

Vinvika [58]3 years ago

6 0

Answer:

The possible lengths are all the real numbers greater than 4 inches and less than 20 inches

Step-by-step explanation:

we know that

<u>The Triangle Inequality Theorem</u> states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Let

c----> the length of the third side of triangle

Applying the triangle inequality theorem

1) 12+8 > c

20 > c

Rewrite

c < 20 in

2) 8+c > 12

c > 12-8

c < 4 in

therefore

4 in < c < 20 in

The possible lengths are all the real numbers greater than 4 inches and less than 20 inches

katrin [286]3 years ago

5 0

Answer:

The third side must be smaller than 20 inches and greater than 4 inches

$4$

Step-by-step explanation:

Let a, b and c be the lengths of triangle's sides. Then

$a+b>c\\ \\a+c>b\\ \\b+c>a$

Use this rule in your case. So, if a=12 and b=8, then

$12+8>c\\ \\12+c>8\\ \\8+c>12$

Hence, you get

$c-4\\ \\c>4$

From these inequalities, you can state that

$4$

So, c must be smaller than 20 inches and greater than 4 inches.

You might be interested in

PLEASE HELP!!! Trapezoid ABCD was dilated to create trapezoid A'B'C'D'. Which statements are true about the trapezoids? Check al

hichkok12 [17]

Answer:

Option A , B and D are true.

The statement which are true:

The length of side AD is 4 units

The length of side A'D' is 8 units.

The scale factor is, $\frac{1}{2}$

Step-by-step explanation:

Given in figure trapezoid ABCD;

The coordinates of ABCD are:

A= (-4, 0)

B = (-2, 4)

C = (2,4)

D = (4, 0)

Since, trapezoid ABCD was dilated to create trapezoid A'B'C'D' as shown in figure;

The coordinates of A'B'C'D' are;

A' =(-2, 0)

B'=(-1, 2)

C' = (1, 2)

D' = (2, 0)

First calculate the length of AD

Using Distance formula for any two points i.e,

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Since, A = (-4, 0) and D = (4, 0)

then;

Length of AD = $\sqrt{(4-(-4))^2+(0-0)^2} = \sqrt{(4+4)^2} =\sqrt{64}=8$ units

Therefore, the length of side AD is, 8 units.

Similarly find the length of A'D'.

Where A' = (-2, 0) and D' =(2,0)

Using distance formula:

Length of A'D' = $\sqrt{(2-(-2))^2+(0-0)^2} =\sqrt{(2+2)^2}= \sqrt{4^2} = 4$

Therefore, the length of side A'D' is, 4 units.

Now, find the slope of CD and C'D'

where C =(2, 4) , D = (4, 0) , C' = (1, 2) and D' =(2,0)

using slope formula for any two points is given by:

$Slope = \frac{y_2-y_1}{x_2-x_1}$

$Slope of CD = \frac{0-4}{4-2} = \frac{-4}{2} = -2$

Similarly,

$Slope of C'D' = \frac{0-2}{2-1} = \frac{-4}{2} = -2$

Since, Sides CD and C'D' have same slope i.e, -2

Scale factor(k) states that every coordinate of the original figure has been multiplied by the scale factor.

If k > 1, then the image is an enlargement.

if 0<k< 1, then the image is a reduction.

If k = 1, then the figure and the image are congruent.

The rule for dilation with scale factor(k) is;

$(x, y) \rightarrow (kx , ky)$

To find the scale factor:

A = (-4, 0) and A' = (-2, 0)

$(-2, 0) \rightarrow (-4k , 0)$

On comparing we ghet;

-4k = -2

Divide -4 both sides we get;

$k = \frac{1}{2}$

∴ The Scale factor is, $k = \frac{1}{2}$

Since, k < 1 which implies the image is a reduction.

Therefore, the statements which are true regarding about trapezoids are;

The length of side AD is 4 units

The length of side A'D' is 8 units.

The scale factor is, $\frac{1}{2}$

6 0

2 years ago

Pls answer too the problem

astra-53 [7]

Answer:

your answer is c

Step-by-step explanation:

7 0

3 years ago

Thx for all the help yall's help

mina [271]

Follow the link above.

3 0

2 years ago

Read 2 more answers

Elodia [21]

Answer:

B. -55

Step-by-step explanation:

La resta entre ambas funciones consiste en la sustracción de términos semejantes como demostraremos a continuación:

1) $f(x) =-2\cdot x ^{2}-6$ Dado

2) $g(x) = x+4$ Dado

3) $(f-g)(x) = (-2\cdot x^{2}-6)-(x+4)$ Definición de resta de funciones.

4) $(f-g)(x) = (-2\cdot x^{2}-6)+(-1) \cdot (x+4)$ $(-1)\cdot a = -a$

5) $(f-g)(x) = (-2\cdot x^{2}-6) + (-x-4)$ Propiedad distributiva/ $(-1)\cdot a = -a$

6) $(f-g)(x) = -2\cdot x^{2}-x+(-6-4)$ Propiedad conmutativa

7) $(f-g) (x) = -2\cdot x^{2}-x-10$ Sustracción de términos semejantes/Resultados.

A continuación, evaluamos la función resultante en $x = -5$ :

$(f-g)(-5) = -2\cdot (-5)^{2}-(-5)-10$

$(f-g)(-5) =-55$

Por ende, la respuesta correcta es B.

8 0

2 years ago

Which is greater 3/7 3/6 3/5

Elanso [62]

3/7= 0.428571

3/6= 0.5

3/5= 0.6

So 3/5 is the greatest of all of them.

8 0

3 years ago

Read 2 more answers